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Conference articles
2017
  1. N.S. Kumar, M. A. Al-Radhawi, D. Del Vecchio, and E. D. Sontag. Stochasticity is necessary for multiple attractors in a class of differentiation networks. In 2017 American Control Conference (ACC), pages submitted, 2017. Keyword(s): systems biology, genetic regulatory, multistability, gene networks.
    Abstract:
    Deterministic models remain the most common option for modeling gene regulatory networks even when the underlying assumptions of high copy numbers and fast promoter kinetics are unsatisfied. Here, we analyze a widely studied differentiation network motif known as the PU.1-GATA-1 circuit and we show that an ODE model of the biomolecular reactions consistent with known biology is incapable of exhibiting multistability, a defining behaviour for such a network. Thus, we consider the chemical master equation model of the same biomolecular reactions and using results recently developed by the authors, we analytically construct the stationary distribution. We show that this distribution is indeed capable of admitting a multitude of modes. We illustrate the results with a numerical example.


2016
  1. M. Lang and E.D. Sontag. Scale-invariant systems realize nonlinear differential operators. In 2016 American Control Conference (ACC), pages 6676 - 6682, 2016. [PDF] Keyword(s): scale invariance, fold change detection, nonlinear systems, realization theory, internal model principle.
    Abstract:
    In this article, we show that scale-invariant systems, as well as systems invariant with respect to other input transformations, can realize nonlinear differential operators: when excited by inputs obeying functional forms characteristic for a given class of invariant systems, the systems' outputs converge to constant values directly quantifying the speed of the input.


  2. F. Menolascina, R. Stocker, and E.D. Sontag. In-vivo identification and control of aerotaxis in Bacillus subtilis. In Proc. IEEE Conf. Decision and Control, Dec. 2016, pages 764-769, 2016. [PDF] Keyword(s): identification, systems biology, aerotaxis, B. subtilis.
    Abstract:
    Combining in-vivo experiments with system identification methods, we determine a simple model of aerotaxis in B. subtilis, and we subsequently employ this model in order to compute the sequence of oxygen gradients needed in order to achieve set-point regulation with respect to a signal tracking the center of mass of the bacterial population. We then successfully validate both the model and the control scheme, by showing that in-vivo positioning control can be achieved via the application of the precomputed inputs in-vivo in an open-loop configuration.


  3. E.D. Sontag. Some remarks on immune control of infections and tumors. In Proc. IEEE Conf. Decision and Control, Dec. 2016, pages 2476-2480, 2016. Keyword(s): scale invariance, fold change detection, T cells, incoherent feedforward loops, immunology, cancer.


  4. Q. Tyles, T. Kang, E.D. Sontag, and L. Bleris. Exploring the impact of resource limitations on gene network reconstruction. In Proc. IEEE Conf. Decision and Control, Dec. 2016, pages 3350-3355, 2016. [PDF] Keyword(s): Biological systems, Genetic regulatory systems, Systems biology.
    Abstract:
    Applying Modular Response Analysis to a synthetic gene circuit, which was introduced in a recent paper by the authors, leads to the inference of a nontrivial "ghost" regulation edge which was not explicitly engineered into the network and which is, in fact, not immediately apparent from experimental measurements. One may thus hypothesize that this ghost regulatory effect is due to competition for resources. A mathematical model is proposed, and analyzed in closed form, that lends validation to this hypothesis.


  5. Y. Zarai, M. Margaliot, E.D. Sontag, and T. Tuller. Controlling the ribosomal density profile in mRNA translation. In Proc. IEEE Conf. Decision and Control, Dec. 2016, pages 4184-4189, 2016. Keyword(s): ribosomes, translation.


2015
  1. A. O. Hamadeh, E.D. Sontag, and D. Del Vecchio. A contraction approach to output tracking via high-gain feedback. In Proc. IEEE Conf. Decision and Control, Dec. 2015, pages 7689-7694, 2015. [PDF]
    Abstract:
    This paper adopts a contraction approach to the analysis of the tracking properties of dynamical systems under high gain feedback when subject to inputs with bounded derivatives. It is shown that if the tracking error dynamics are contracting, then the system is input to output stable with respect to the input signal derivatives and the output tracking error. As an application, it iss hown that the negative feedback connection of plants composed of two strictly positive real LTI subsystems in cascade can follow external inputs with tracking errors that can be made arbitrarily small by applying a sufficiently large feedback gain. We utilize this result to design a biomolecular feedback for a synthetic genetic sensor to make it robust to variations in the availability of a cellular resource required for protein production.


2014
  1. Z. Aminzare and E.D. Sontag. Contraction methods for nonlinear systems: A brief introduction and some open problems. In Proc. IEEE Conf. Decision and Control, Los Angeles, Dec. 2014, pages 3835-3847, 2014. [PDF] Keyword(s): contractions, contractive systems, stability, reaction-diffusion PDE's, synchronization, contractive systems, stability.
    Abstract:
    Contraction theory provides an elegant way to analyze the behaviors of certain nonlinear dynamical systems. Under sometimes easy to check hypotheses, systems can be shown to have the incremental stability property that trajectories converge to each other. The present paper provides a self-contained introduction to some of the basic concepts and results in contraction theory, discusses applications to synchronization and to reaction-diffusion partial differential equations, and poses several open questions.


  2. Z. Aminzare and E.D. Sontag. Remarks on diffusive-link synchronization using non-Hilbert logarithmic norms. In Proc. IEEE Conf. Decision and Control, Los Angeles, Dec. 2014, pages 6086-6091, 2014. Keyword(s): contractions, contractive systems, stability, reaction-diffusion PDE's, synchronization.
    Abstract:
    In this paper, we sketch recent results for synchronization in a network of identical ODE models which are diffusively interconnected. In particular, we provide estimates of convergence of the difference in states between components, in the cases of line, complete, and star graphs, and Cartesian products of such graphs.


  3. M. Skataric, E.V. Nikolaev, and E.D. Sontag. Scale-invariance in singularly perturbed systems. In Proc. IEEE Conf. Decision and Control, Los Angeles, Dec. 2014, pages 3035-3040, 2014. [PDF] Keyword(s): singular perturbations, scale invariance, systems biology, transient behavior, symmetries, fcd, fold-change detection.
    Abstract:
    This conference paper (a) summarizes material from "A fundamental limitation to fold-change detection by biological systems with multiple time scales" (IET Systems Biology 2014) and presents additional remarks regarding (b) expansion techniques to compute FCD error and (c) stochastic adaptation and FCD


  4. M. Skataric and E.D. Sontag. Remarks on model-based estimation of nonhomogeneous Poisson processes and applications to biological systems. In Proc. European Control Conference, Strasbourg, France, June 2014, pages 2052-2057, 2014. [PDF] Keyword(s): systems biology, random dynamical systems.
    Abstract:
    This paper studies model-based estimation methods of a rate of a nonhomogeneous Poisson processes that describes events arising from modeling biological phenomena in which discrete events are measured. We describe an approach based on observers and Kalman filters as well as preliminary simulation results, and compare these to other methods (not model-based) in the literature. The problem is motivated by the question of identification of internal states from neural spikes and bacterial tumbling behavior.


  5. E.D. Sontag. Quantifying the effect of interconnections on the steady states of biomolecular networks. In Proc. IEEE Conf. Decision and Control, Los Angeles, Dec. 2014, pages 5419-5424, 2014.


  6. E.D. Sontag, M. Margaliot, and T. Tuller. On three generalizations of contraction. In Proc. IEEE Conf. Decision and Control, Los Angeles, Dec. 2014, pages 1539-1544, 2014. Keyword(s): contractions, contractive systems, stability.
    Abstract:
    We introduce three forms of generalized contraction~(GC). Roughly speaking, these are motivated by allowing contraction to take place after small transients in time and/or amplitude. Indeed, contraction is usually used to prove asymptotic properties, like convergence to an attractor or entrainment to a periodic excitation, and allowing initial transients does not affect this asymptotic behavior. We provide sufficient conditions for GC, and demonstrate their usefulness using examples of systems that are not contractive, with respect to any norm, yet are~GC.


2013
  1. A. O. Hamadeh, E.D. Sontag, and B.P. Ingalls. Response time re-scaling and Weber's law in adapting biological systems. In Proc. American Control Conference, pages 4564-4569, 2013. [PDF] Keyword(s): scale invariance, systems biology, transient behavior, symmetries, fcd, fold-change detection, chemotaxis.
    Abstract:
    Recent experimental work has shown that transient E. coli chemotactic response is unchanged by a scaling of its ligand input signal (fold change detection, or FCD), and this is in agreement with earlier mathematical predictions. However, this prediction was based on certain particular assumptions on the structure of the chemotaxis pathway. In this work, we begin by showing that behavior similar to FCD can be obtained under weaker conditions on the system structure. Namely, we show that under relaxed conditions, a scaling of the chemotaxis system's inputs leads to a time scaling of the output response. We propose that this may be a contributing factor to the robustness of the experimentally observed FCD. We further show that FCD is a special case of this time scaling behavior for which the time scaling factor is unity. We then proceed to extend the conditions for output time scaling to more general adapting systems, and demonstrate this time scaling behavior on a published model of the chemotaxis pathway of the bacterium Rhodobacter sphaeroides. This work therefore provides examples of how robust biological behavior can arise from simple yet realistic conditions on the underlying system structure.


  2. Y. Shafi, Z. Aminzare, M. Arcak, and E.D. Sontag. Spatial uniformity in diffusively-coupled systems using weighted L2 norm contractions. In Proc. American Control Conference, pages 5639-5644, 2013. [PDF] Keyword(s): contractions, contractive systems, matrix measures, logarithmic norms, Turing instabilities, diffusion, partial differential equations, synchronization.
    Abstract:
    We present conditions that guarantee spatial uniformity in diffusively-coupled systems. Diffusive coupling is a ubiquitous form of local interaction, arising in diverse areas including multiagent coordination and pattern formation in biochemical networks. The conditions we derive make use of the Jacobian matrix and Neumann eigenvalues of elliptic operators, and generalize and unify existing theory about asymptotic convergence of trajectories of reaction-diffusion partial differential equations as well as compartmental ordinary differential equations. We present numerical tests making use of linear matrix inequalities that may be used to certify these conditions. We discuss an example pertaining to electromechanical oscillators. The paper's main contributions are unified verifiable relaxed conditions that guarantee synchrony.


  3. M. Marcondes de Freitas and E.D. Sontag. A class of random control systems: Monotonicity and the convergent-input convergent-state property. In Proc. American Control Conference, pages 4564-4569, 2013. [PDF] Keyword(s): random dynamical systems, monotone systems.


2012
  1. D. Angeli and E.D. Sontag. Remarks on the invalidation of biological models using monotone systems theory. In Proc. IEEE Conf. Decision and Control, Maui, Dec. 2012, 2012. Note: Paper TuC09.3.[PDF]
    Abstract:
    This paper presents techniques for finding out what type of solutions are compatible with a given sign pattern of interactions between state/input variables once the input behaviour is also known. By ``type'' of solutions we essentially refer to the sequence of upwards or downwards segments that variables can exhibit (essentially sign-patterns of variables derivatives) once input profiles are also specified. A concrete experimental example of how such techniques can invalidate models is also provided.


  2. A.O. Hamadeh, B.P. Ingalls, and E.D. Sontag. Fold-Change Detection As a Chemotaxis Model Discrimination Tool. In Proc. IEEE Conf. Decision and Control, Maui, Dec. 2012, 2012. Note: Paper WeC09.2.Keyword(s): scale invariance, systems biology, transient behavior, symmetries, fcd, fold-change detection, chemotaxis.


  3. A. Rufino Ferreira, M. Arcak, and E.D. Sontag. A decomposition-based approach to stability analysis of large-scale stochastic systems. In Proceedings of the 2012 American Control Conference, Montreal, June 2012, pages Paper FrC10.4, 2012. Keyword(s): stochastic systems, passivity, noise-to-state stability.
    Abstract:
    Conference version of ``Stability certification of large scale stochastic systems using dissipativity of subsystems''.


  4. M. Skataric and E.D. Sontag. Exploring the scale invariance property in enzymatic networks. In Proc. IEEE Conf. Decision and Control, Maui, Dec. 2012, 2012. Note: Paper WeC09.2.Keyword(s): scale invariance, systems biology, transient behavior, symmetries, fcd, fold-change detection, enzymatic networks.
    Abstract:
    This is a conference version of ``A characterization of scale invariant responses in enzymatic networks.


2011
  1. D. Angeli and E.D. Sontag. A small-gain result for orthant-monotone systems in feedback: the non sign-definite case. In Proc. IEEE Conf. Decision and Control, Orlando, Dec. 2011, pages WeC09.1, 2011. Keyword(s): small-gain theorem, monotone systems.
    Abstract:
    This note introduces a small-gain result for interconnected MIMO orthant-monotone systems for which no matching condition is required between the partial orders in input and output spaces of the considered subsystems. Previous results assumed that the partial orders adopted would be induced by positivity cones in input and output spaces and that such positivity cones should fulfill a compatibility rule: namely either be coincident or be opposite. Those two configurations corresponded to positive-feedback or negative feedback cases. We relax those results by allowing arbitrary orthant orders.


  2. O. Shoval, U. Alon, and E.D. Sontag. Input symmetry invariance, and applications to biological systems. In Proc. IEEE Conf. Decision and Control, Orlando, Dec. 2011, pages TuA02.5, 2011. Keyword(s): adaptation, feedforward loops, integral feedback, scale invariance, systems biology, transient behavior, symmetries, fcd, fold-change detection, jump Markov processes.
    Abstract:
    This paper studies invariance with respect to symmetries in sensory fields, a particular case of which, scale invariance, has recently been found in certain eukaryotic as well as bacterial cell signaling systems. We describe a necessary and sufficient characterization of symmetry invariance in terms of equivariant transformations, show how this characterization helps find all possible symmetries in standard models of biological adaptation, and discuss symmetry-invariant searches.


2010
  1. G. Russo, M. di Bernardo, and E.D. Sontag. Stability of networked systems: a multi-scale approach using contraction. In Proc. IEEE Conf. Decision and Control, Atlanta, Dec. 2010, pages FrB14.3, 2010. Keyword(s): contractive systems, contractions, systems biology, biochemical networks, synchronization.
    Abstract:
    Preliminary conference version of ''A contraction approach to the hierarchical analysis and design of networked systems''.


  2. E.D. Sontag. Remarks on structural identification, modularity, and retroactivity. In Proc. IEEE Conf. Decision and Control, Atlanta, Dec. 2010, pages ThA23.1, 2010. [PDF] Keyword(s): modularity, retroactivity, identification.
    Abstract:
    Summarized conference version of ``Modularity, retroactivity, and structural identification''.


  3. A. White, P.G. Cipriani, H.-L. Kao, B. Lees, D. Geiger, E.D. Sontag, K. Gunsalus, and F. Piano. Rapid and accurate developmental stage recognition of C. elegans from high-throughput image data. In 2010 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 3089-3096, 2010. [PDF]
    Abstract:
    This paper presents a hierarchical principle for object recognition and its application to automatically classify developmental stages of C. elegans animals from a population of mixed stages. The system is in current use in a functioning C. elegans laboratory and has processed over two hundred thousand images for lab users.


2009
  1. D. Angeli, P. de Leenheer, and E.D. Sontag. On persistence of chemical reaction networks with time-dependent kinetics and no global conservation laws. In Proc. IEEE Conf. Decision and Control, Shanhai, Dec. 2009, pages 4559-4564, 2009. [PDF] Keyword(s): biochemical networks, fluxes, Petri nets, persistence, biochemical networks with inputs.
    Abstract:
    This is a very summarized version ofthe first part of the paper "Persistence results for chemical reaction networks with time-dependent kinetics and no global conservation laws".


  2. L. Scardovi, M. Arcak, and E.D. Sontag. Synchronization of interconnected systems with an input-output approach. Part I: Main results. In Proc. IEEE Conf. Decision and Control, Shanhai, Dec. 2009, pages 609-614, 2009. Note: First part of conference version of journal paper.Keyword(s): passive systems, secant condition, biochemical networks, systems biology.
    Abstract:
    See abstract and link to pdf in entry for Journal paper.


  3. L. Scardovi, M. Arcak, and E.D. Sontag. Synchronization of interconnected systems with an input-output approach. Part II: State-Space result and application to biochemical networks. In Proc. IEEE Conf. Decision and Control, Shanhai, Dec. 2009, pages 615-620, 2009. Note: Second part of conference version of journal paper.Keyword(s): passive systems, secant condition, biochemical networks, systems biology.
    Abstract:
    See abstract and link to pdf in entry for Journal paper.


2008
  1. B. Andrews, E.D. Sontag, and P. Iglesias. An approximate internal model principle: Applications to nonlinear models of biological systems. In Proc. 17th IFAC World Congress, Seoul, pages Paper FrB25.3, 6 pages, 2008. [PDF] Keyword(s): biological adaptation, internal model principle.
    Abstract:
    The proper function of many biological systems requires that external perturbations be detected, allowing the system to adapt to these environmental changes. It is now well established that this dual detection and adaptation requires that the system have an internal model in the feedback loop. In this paper we relax the requirement that the response of the system adapt perfectly, but instead allow regulation to within a neighborhood of zero. We show, in a nonlinear setting, that systems with the ability to detect input signals and approximately adapt require an approximate model of the input. We illustrate our results by analyzing a well-studied biological system. These results generalize previous work which treats the perfectly adapting case.


  2. D. Del Vecchio, A.J. Ninfa, and E.D. Sontag. A Systems Theory with Retroactivity: Application to Transcriptional Modules. In Proceedings of the 2008 American Control Conference, Seattle, June 2008, pages Paper WeC04.1, 2008. [PDF] Keyword(s): retroactivity, systems biology, biochemical networks, synthetic biology, futile cycles, singular perturbations, modularity.


  3. L. Wang, P. de Leenheer, and E.D. Sontag. Global stability for monotone tridiagonal systems with negative feedback. In Proc. IEEE Conf. Decision and Control, Cancun, Dec. 2008, pages 4091-4096, 2008. Keyword(s): systems biology, monotone systems, tridiagonal systems, global stability.
    Abstract:
    Conference version of paper "Conditions for global stability of monotone tridiagonal systems with negative feedback"


2007
  1. D. Angeli, P. de Leenheer, and E.D. Sontag. Petri nets tools for the analysis of persistence in chemical networks. In Proc. 7th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2007), Pretoria, South Africa, 22-24 August, 2007, 2007. Keyword(s): Petri nets, systems biology, biochemical networks, nonlinear stability, dynamical systems, futile cycles.


  2. M. Arcak and E.D. Sontag. A passivity-based stability criterion for a class of interconnected systems and applications to biochemical reaction networks. In Proc. IEEE Conf. Decision and Control, New Orleans, Dec. 2007, pages 4477-4482, 2007. Note: Conference version of journal paper with same title. Keyword(s): systems biology, biochemical networks, cyclic feedback systems, secant condition, nonlinear stability, dynamical systems.


  3. D. Del Vecchio and E.D. Sontag. Dynamics and control of synthetic bio-molecular networks. In Proceedings American Control Conf., New York, July 2007, pages 1577-1588, 2007. Keyword(s): systems biology, biochemical networks, synthetic biology.
    Abstract:
    This tutorial paper presents an introduction to systems and synthetic molecular biology. It provides an introduction to basic biological concepts, and describes some of the techniques as well as challenges in the analysis and design of biomolecular networks.


  4. M.R. Jovanovic, M. Arcak, and E.D. Sontag. Remarks on the stability of spatially distributed systems with a cyclic interconnection structure. In Proceedings American Control Conf., New York, July 2007, pages 2696-2701, 2007. Keyword(s): systems biology, biochemical networks, cyclic feedback systems, spatially distributed systems, secant condition.
    Abstract:
    For distributed systems with a cyclic interconnection structure, a global stability result is shown to hold if the secant criterion is satisfied.


  5. E.D. Sontag, Y. Wang, and A. Megretski. Remarks on Input Classes for Identification of Bilinear Systems. In Proceedings American Control Conf., New York, July 2007, pages 4345-4350, 2007. Keyword(s): realization theory, observability, identifiability, bilinear systems.


  6. L. Wang and E.D. Sontag. Further results on singularly perturbed monotone systems, with an application to double phosphorylation cycles. In Proc. IEEE Conf. Decision and Control, New Orleans, Dec. 2007, pages 627-632, 2007. Note: Conference version of Singularly perturbed monotone systems and an application to double phosphorylation cycles.Keyword(s): singular perturbations, futile cycles, MAPK cascades, systems biology, biochemical networks, nonlinear stability, nonlinear dynamics, multistability, monotone systems.


2006
  1. B. Andrews, P. Iglesias, and E.D. Sontag. Signal detection and approximate adaptation implies an approximate internal model. In Proc. IEEE Conf. Decision and Control, San Diego, Dec. 2006, pages 2364-2369, 2006. IEEE. [PDF] Keyword(s): biological adaptation, internal model principle.
    Abstract:
    This conference paper presented a version of an approximate internal model principle, for linear systems. A subsequent paper at the IFAC 2008 conference improved on this result by extending it to a class of nonlinear systems.


  2. D. Angeli and E.D. Sontag. A note on monotone systems with positive translation invariance. In Control and Automation, 2006. MED '06. 14th Mediterranean Conference on, 28-30 June 2006, pages 1-6, 2006. IEEE. Note: Available from ieeexplore.ieee.org. [PDF] [doi:10.1109/MED.2006.3287822B2B2B2B2B2B] Keyword(s): systems biology, biochemical networks, nonlinear stability, dynamical systems, monotone systems.
    Abstract:
    Strongly monotone systems of ordinary differential equations which have a certain translation-invariance property are shown to have the property that all projected solutions converge to a unique equilibrium. This result may be seen as a dual of a well-known theorem of Mierczynski for systems that satisfy a conservation law. As an application, it is shown that enzymatic futile cycles have a global convergence property.


  3. D. Angeli, P. de Leenheer, and E.D. Sontag. On the structural monotonicity of chemical reaction networks. In Proc. IEEE Conf. Decision and Control, San Diego, Dec. 2006, pages 7-12, 2006. IEEE. [PDF] Keyword(s): monotone systems, systems biology, biochemical networks, nonlinear stability, dynamical systems.
    Abstract:
    This paper derives new results for certain classes of chemical reaction networks, linking structural to dynamical properties. In particular, it investigates their monotonicity and convergence without making assumptions on the structure (e.g., mass-action kinetics) of the dynamical equations involved, and relying only on stoichiometric constraints. The key idea is to find a suitable set of coordinates under which the resulting system is cooperative. As a simple example, the paper shows that a phosphorylation/dephosphorylation process, which is involved in many signaling cascades, has a global stability property.


  4. M. Arcak and E.D. Sontag. Connections between diagonal stability and the secant condition for cyclic systems. In Proc. American Control Conference, Minneapolis, June 2006, pages 1493-1498, 2006. Keyword(s): systems biology, biochemical networks, cyclic feedback systems, secant condition, nonlinear stability, dynamical systems.


  5. M. Chaves, E.D. Sontag, and R. Albert. Structure and timescale analysis in genetic regulatory networks. In Proc. IEEE Conf. Decision and Control, San Diego, Dec. 2006, pages 2358-2363, 2006. IEEE. [PDF] Keyword(s): genetic regulatory networks, Boolean systems, hybrid systems.
    Abstract:
    This work is concerned with the study of the robustness and fragility of gene regulation networks to variability in the timescales of the distinct biological processes involved. It explores and compares two methods: introducing asynchronous updates in a Boolean model, or integrating the Boolean rules in a continuous, piecewise linear model. As an example, the segment polarity network of the fruit fly is analyzed. A theoretical characterization is given of the model's ability to predict the correct development of the segmented embryo, in terms of the specific timescales of the various regulation interactions.


  6. L. Wang and E.D. Sontag. A remark on singular perturbations of strongly monotone systems. In Proc. IEEE Conf. Decision and Control, San Diego, Dec. 2006, pages 989-994, 2006. IEEE. [PDF] Keyword(s): systems biology, biochemical networks, nonlinear stability, dynamical systems, singular perturbations, monotone systems.
    Abstract:
    This paper deals with global convergence to equilibria, and in particular Hirsch's generic convergence theorem for strongly monotone systems, for singular perturbations of monotone systems.


  7. L. Wang and E.D. Sontag. Almost global convergence in singular perturbations of strongly monotone systems. In C. Commault and N. Marchand, editors, Positive Systems, pages 415-422, 2006. Springer-Verlag, Berlin/Heidelberg. Note: (Lecture Notes in Control and Information Sciences Volume 341, Proceedings of the second Multidisciplinary International Symposium on Positive Systems: Theory and Applications (POSTA 06) Grenoble, France). [PDF] [doi:10.1007/3-540-34774-7] Keyword(s): systems biology, biochemical networks, nonlinear stability, dynamical systems, singular perturbations, monotone systems.
    Abstract:
    This paper deals with global convergence to equilibria, and in particular Hirsch's generic convergence theorem for strongly monotone systems, for singular perturbations of monotone systems.


2005
  1. G.A. Enciso and E.D. Sontag. A remark on multistability for monotone systems II. In Proc. IEEE Conf. Decision and Control, Seville, Dec. 2005, IEEE Publications, pages 2957-2962, 2005. Keyword(s): multistability, systems biology, biochemical networks, nonlinear stability, dynamical systems, monotone systems.


  2. E.D. Sontag. A notion of passivity gain and a generalization of the `secant condition' for stability. In Proc. IEEE Conf. Decision and Control, Seville, Dec. 2005, IEEE Publications, pages 5645-5649, 2005. Keyword(s): nonlinear stability, dynamical systems.


  3. E.D. Sontag and M. Chaves. Computation of amplification for systems arising from cellular signaling pathways. In Proc. 16th IFAC World Congress, Prague, July 2005, 2005. Keyword(s): systems biology, biochemical networks, dynamical systems.


2004
  1. D. Angeli and E.D. Sontag. An analysis of a circadian model using the small-gain approach to monotone systems. In Proc. IEEE Conf. Decision and Control, Paradise Island, Bahamas, Dec. 2004, IEEE Publications, pages 575-578, 2004. [PDF] Keyword(s): circadian rhythms, tridiagonal systems, nonlinear dynamics, systems biology, biochemical networks, oscillations, periodic behavior, monotone systems.
    Abstract:
    We show how certain properties of Goldbeter's original 1995 model for circadian oscillations can be proved mathematically. We establish global asymptotic stability, and in particular no oscillations, if the rate of transcription is somewhat smaller than that assumed by Goldbeter, but, on the other hand, this stability persists even under arbitrary delays in the feedback loop. We are mainly interested in illustrating certain mathematical techniques, including the use of theorems concerning tridiagonal cooperative systems and the recently developed theory of monotone systems with inputs and outputs.


  2. D. Angeli, P. de Leenheer, and E.D. Sontag. A tutorial on monotone systems- with an application to chemical reaction networks. In Proc. 16th Int. Symp. Mathematical Theory of Networks and Systems (MTNS 2004), CD-ROM, WP9.1, Katholieke Universiteit Leuven, 2004. [PDF] Keyword(s): systems biology, biochemical networks, nonlinear stability, dynamical systems, monotone systems.
    Abstract:
    Monotone systems are dynamical systems for which the flow preserves a partial order. Some applications will be briefly reviewed in this paper. Much of the appeal of the class of monotone systems stems from the fact that roughly, most solutions converge to the set of equilibria. However, this usually requires a stronger monotonicity property which is not always satisfied or easy to check in applications. Following work of J.F. Jiang, we show that monotonicity is enough to conclude global attractivity if there is a unique equilibrium and if the state space satisfies a particular condition. The proof given here is self-contained and does not require the use of any of the results from the theory of monotone systems. We will illustrate it on a class of chemical reaction networks with monotone, but otherwise arbitrary, reaction kinetics.


  3. D. Angeli, P. de Leenheer, and E.D. Sontag. Remarks on monotonicity and convergence in chemical reaction networks. In Proc. IEEE Conf. Decision and Control, Paradise Island, Bahamas, Dec. 2004, IEEE Publications, pages 243-248, 2004. Keyword(s): systems biology, biochemical networks, nonlinear stability, dynamical systems, monotone systems.


  4. M. Chaves, E.D. Sontag, and R.J. Dinerstein. Gains and optimal design in signaling pathways. In Proc. IEEE Conf. Decision and Control, Paradise Island, Bahamas, Dec. 2004, IEEE Publications, pages 596-601, 2004. Keyword(s): systems biology, biochemical networks, dynamical systems.


  5. B. DasGupta, J.P. Hespanha, and E.D. Sontag. Aggregation-based approaches to honey-pot searching with local sensory information. In Proceedings American Control Conf., Boston, June 2004, 2004. Note: (CD-ROM WeM17.4, IEEE Publications, Piscataway). [PDF]
    Abstract:
    We investigate the problem of searching for a hidden target in a bounded region by an autonomous agent that is only able to use limited local sensory information. We propose an aggregation-based approach to solve this problem, in which the continuous search space is partitioned into a finite collection of regions on which we define a discrete search problem. A solution to the original problem is then obtained through a refinement procedure that lifts the discrete path into a continuous one. The resulting solution is in general not optimal but one can construct bounds to gauge the cost penalty incurred.


  6. B. DasGupta, J.P. Hespanha, and E.D. Sontag. Computational complexities of honey-pot searching with local sensory information. In Proceedings American Control Conf., Boston, June 2004, CD-ROM, ThA06.1, IEEE Publications, Piscataway, 2004. [PDF]
    Abstract:
    In this paper we investigate the problem of searching for a hidden target in a bounded region of the plane, by an autonomous robot which is only able to use limited local sensory information. We formalize a discrete version of the problem as a "reward-collecting" path problem and provide efficient approximation algorithms for various cases.


  7. G.A. Enciso and E.D. Sontag. A remark on multistability for monotone systems. In Proc. IEEE Conf. Decision and Control, Paradise Island, Bahamas, Dec. 2004, IEEE Publications, pages 249-254, 2004. Keyword(s): multistability, systems biology, biochemical networks, nonlinear stability, dynamical systems, monotone systems.


  8. J.L. Mancilla-Aguilar, R. Garcìa, E.D. Sontag, and Y. Wang. Representation of switched systems by perturbed control systems. In Proc. IEEE Conf. Decision and Control, Paradise Island, Bahamas, Dec. 2004, IEEE Publications, pages 3259-3264, 2004.


2003
  1. D. Angeli and E.D. Sontag. A note on multistability and monotone I/O systems. In Proc. IEEE Conf. Decision and Control, Maui, Dec. 2003, IEEE Publications, 2003, pages 67-72, 2003. Keyword(s): systems biology, biochemical networks, nonlinear stability, dynamical systems, monotone systems.


  2. M. Malisoff, L. Rifford, and E.D. Sontag. Remarks on input to state stabilization. In Proc. IEEE Conf. Decision and Control, Maui, Dec. 2003, IEEE Publications, 2003, pages 1053-1058, 2003. [PDF] Keyword(s): nonlinear control, feedback stabilization.


  3. L. Moreau, E.D. Sontag, and M. Arcak. How feedback can tune a bifurcation parameter towards its unknown critical bifurcation value. In Proc. IEEE Conf. Decision and Control, Maui, Dec. 2003, IEEE Publications, 2003, pages 2401-2406, 2003.


2002
  1. D. Angeli and E.D. Sontag. A remark on monotone control systems. In Proc. IEEE Conf. Decision and Control, Las Vegas, Dec. 2002, IEEE Publications, pages 1876-1881, 2002.


  2. J.P. Hespanha, D. Liberzon, and E.D. Sontag. Nonlinear observability and an invariance principle for switched systems. In Proc. IEEE Conf. Decision and Control, Las Vegas, Dec. 2002, IEEE Publications, pages 4300-4305, 2002. [PDF] Keyword(s): observability.


  3. B.P. Ingalls, E.D. Sontag, and Y. Wang. A relaxation theorem for differential inclusions with applications to stability properties. In D. Gilliam and J. Rosenthal, editors, Mathematical Theory of Networks and Systems, Electronic Proceedings of MTNS-2002 Symposium held at the University of Notre Dame, August 2002, 2002. Note: (12 pages). [PDF]
    Abstract:
    The fundamental Filippov--Wazwski Relaxation Theorem states that the solution set of an initial value problem for a locally Lipschitz inclusion is dense in the solution set of the same initial value problem for the corresponding relaxation inclusion on compact intervals. In a recent paper of ours, a complementary result was provided for inclusions with finite dimensional state spaces which says that the approximation can be carried out over non-compact or infinite intervals provided one does not insist on the same initial values. This note extends the infinite-time relaxation theorem to the inclusions whose state spaces are Banach spaces. To illustrate the motivations for studying such approximation results, we briefly discuss a quick application of the result to output stability and uniform output stability properties.


  4. B.P. Ingalls, E.D. Sontag, and Y. Wang. Measurement to error stability: a notion of partial detectability for nonlinear systems. In Proc. IEEE Conf. Decision and Control, Las Vegas, Dec. 2002, IEEE Publications, pages 3946-3951, 2002. [PDF] Keyword(s): input to state stability.
    Abstract:
    For systems whose output is to be kept small (thought of as an error output), the notion of input to output stability (IOS) arises. Alternatively, when considering a system whose output is meant to provide information about the state (i.e. a measurement output), one arrives at the detectability notion of output to state stability (OSS). Combining these concepts, one may consider a system with two types of outputs, an error and a measurement. This leads naturally to a notion of partial detectability which we call measurement to error stability (MES). This property characterizes systems in which the error signal is detectable through the measurement signal. This paper provides a partial Lyapunov characterization of the MES property. A closely related property of stability in three measures (SIT) is introduced, which characterizes systems for which the error decays whenever it dominates the measurement. The SIT property is shown to imply MES, and the two are shown to be equivalent under an additional boundedness assumption. A nonsmooth Lyapunov characterization of the SIT property is provided, which yields the partial characterization of MES. The analysis is carried out on systems described by differential inclusions -- implicitly incorporating a disturbance input with compact value-set.


  5. E.D. Sontag. Asymptotic amplitudes, Cauchy gains, an associated small-gain principle, and an application to inhibitory biological feedback. In Proc. IEEE Conf. Decision and Control, Las Vegas, Dec. 2002, IEEE Publications, pages 4318-4323, 2002. Keyword(s): cyclic feedback systems, small-gain.


2001
  1. D. Angeli, E.D. Sontag, and Y. Wang. A note on input-to-state stability with input derivatives. In Proc. Nonlinear Control System Design Symposium, St. Petersburg, July 2001, pages 720-725, 2001. Keyword(s): input to state stability.


  2. M. Arcak, D. Angeli, and E.D. Sontag. Stabilization of cascades using integral input-to-state stability. In Proc. IEEE Conf. Decision and Control, Orlando, Dec. 2001, IEEE Publications, 2001, pages 3814-3819, 2001. Keyword(s): nonlinear control, feedback stabilization, input to state stability.


  3. M. Chaves and E.D. Sontag. An alternative observer for zero deficiency chemical networks. In Proc. Nonlinear Control System Design Symposium, St. Petersburg, July 2001, pages 575-578, 2001. Keyword(s): observability, observers, zero-deficiency networks, systems biology, biochemical networks, nonlinear stability, dynamical systems.


  4. M. Chaves and E.D. Sontag. Observers for certain chemical reaction networks. In Proc. 2001 European Control Conf., Sep. 2001, pages 3715-3720, 2001. Keyword(s): zero-deficiency networks, systems biology, biochemical networks, nonlinear stability, dynamical systems, observability, observers.


  5. M. Chyba, N.E. Leonard, and E.D. Sontag. Optimality for underwater vehicles. In Proc. IEEE Conf. Decision and Control, Orlando, Dec. 2001,IEEE Publications, 2001, pages 4204-4209, 2001. [PDF] Keyword(s): optimal control.


  6. B.P. Ingalls, D. Angeli, E.D. Sontag, and Y. Wang. Asymptotic characterizations of IOSS. In Proc. IEEE Conf. Decision and Control, Orlando, Dec. 2001, IEEE Publications, 2001, pages 881-886, 2001. Keyword(s): nonlinear control, feedback stabilization, input to state stability.


  7. P. Kuusela, D. Ocone, and E.D. Sontag. Remarks on the sample complexity for linear control systems identification. In IFAC Workshop on Adaptation and Learning in Control and Signal Processing, ALCOSP2001, Cernobbio-Como, Italy, 29-31 August, 2001, pages 431-436, 2001.


  8. D. Liberzon, A.S. Morse, and E.D. Sontag. Output-input stability: a new variant of the minimum-phase property for nonlinear systems. In Proc. Nonlinear Control System Design Symposium, St. Petersburg, July 2001, pages 743-748, 2001. Keyword(s): input to state stability.


  9. E.D. Sontag, B.P. Ingalls, and Y. Wang. Generalizations of asymptotic gain characterizations of ISS to input-to-output stability. In Proc. American Control Conf., Arlington, June 2001, pages 2279-2284, 2001. Keyword(s): input to state stability.


2000
  1. M. Chyba, N.E. Leonard, and E.D. Sontag. Time-optimal control for underwater vehicles. In N.E. Leonard and R. Ortega, editors, Lagrangian and Hamiltonian Methods for Nonlinear Control, pages 117-122, 2000. Pergamon Press, Oxford. [PDF]


  2. D. Liberzon, A.S. Morse, and E.D. Sontag. A new definition of the minimum-phase property for nonlinear systems, with an application to adaptive control. In Proc. IEEE Conf. Decision and Control, Sydney, Dec. 2000, IEEE Publications, 2000, pages 2106-2111, 2000.


  3. T. Natschläger, W. Maass, E.D. Sontag, and A. Zador. Processing of time series by neural circuits with biologically realistic synaptic dynamics. In Todd K. Leen, Thomas G. Dietterich, and Volker Tresp, editors, Advances in Neural Information Processing Systems 13 (NIPS2000), pages 145-151, 2000. MIT Press, Cambridge. [PDF] Keyword(s): neural networks, Volterra series.
    Abstract:
    Experimental data show that biological synapses are dynamic, i.e., their weight changes on a short time scale by several hundred percent in dependence of the past input to the synapse. In this article we explore the consequences that this synaptic dynamics entails for the computational power of feedforward neural networks. It turns out that even with just a single hidden layer such networks can approximate a surprisingly large large class of nonlinear filters: all filters that can be characterized by Volterra series. This result is robust with regard to various changes in the model for synaptic dynamics. Furthermore we show that simple gradient descent suffices to approximate a given quadratic filter by a rather small neural system with dynamic synapses.


1999
  1. D. Angeli and E.D. Sontag. Characterizations of forward completeness. In Proc. IEEE Conf. Decision and Control, Phoenix, Dec. 1999, IEEE Publications, 1999, pages 2551-2556, 1999.


  2. L. Grune, E.D. Sontag, and F.R. Wirth. On the equivalence between asymptotic and exponential stability, and between ISS and finite H infinity gain. In Proc. IEEE Conf. Decision and Control, Phoenix, Dec. 1999, IEEE Publications, 1999, pages 1220-1225, 1999. Keyword(s): input to state stability.


  3. B.P. Ingalls, E.D. Sontag, and Y. Wang. Remarks on input to output stability. In Proc. IEEE Conf. Decision and Control, Phoenix, Dec. 1999, IEEE Publications, 1999, pages 1226-1231, 1999. Keyword(s): input to state stability.


  4. Z-P. Jiang, E.D. Sontag, and Y. Wang. Input-to-state stability for discrete-time nonlinear systems. In Proc. 14th IFAC World Congress, Vol E (Beijing), pages 277-282, 1999. [PDF] Keyword(s): input to state stability, input to state stability, discrete-time.
    Abstract:
    This paper studies the input-to-state stability (ISS) property for discrete-time nonlinear systems. We show that many standard ISS results may be extended to the discrete-time case. More precisely, we provide a Lyapunov-like sufficient condition for ISS, and we show the equivalence between the ISS property and various other properties, as well as provide a small gain theorem.


  5. M. Krichman, E.D. Sontag, and Y. Wang. Lyapunov characterizations of input-ouput-to-state stability. In Proc. IEEE Conf. Decision and Control, Phoenix, Dec. 1999, IEEE Publications, 1999, pages 2070-2075, 1999. Keyword(s): input to state stability.


  6. D. Liberzon, E.D. Sontag, and Y. Wang. On integral-input-to-state stabilization. In Proc. American Control Conf., San Diego, June 1999, pages 1598-1602, 1999. [PDF] Keyword(s): input to state stability, control-Lyapunov functions.
    Abstract:
    This paper continues the investigation of the recently introduced integral version of input-to-state stability (iISS). We study the problem of designing control laws that achieve iISS disturbance attenuation. The main contribution is an appropriate concept of control Lyapunov function (iISS-CLF), whose existence leads to an explicit construction of such a control law. The results are compared and contrasted with the ones available for the ISS case.


  7. W. Maass and E.D. Sontag. A precise characterization of the class of languages recognized by neural nets under Gaussian and other common noise distributions. In Proceedings of the 1998 conference on Advances in neural information processing systems II, Cambridge, MA, USA, pages 281-287, 1999. MIT Press. Keyword(s): neural networks.


  8. M. Malisoff and E.D. Sontag. Universal formulas for CLF's with respect to Minkowski balls. In Proc. American Control Conf., San Diego, June 1999, pages 3033-3037, 1999.


  9. D. Nesic, A.R. Teel, and E.D. Sontag. On stability and input-to-state stability ${\cal K}{\cal L}$ estimates of discrete-time and sampled-data nonlinear systems. In Proc. American Control Conf., San Diego, June 1999, pages 3990-3994, 1999. Keyword(s): input to state stability, sampled-data systems, discrete-time systems, sampling.


  10. E.D. Sontag. Feedback insensitive to small measurement errors. In Proc. IEEE Conf. Decision and Control, Phoenix, Dec. 1999, IEEE Publications, 1999, pages 2661-2666, 1999.


1998
  1. D. Angeli, E.D. Sontag, and Y. Wang. A remark on integral input to state stability. In Proc. IEEE Conf. Decision and Control, Tampa, Dec. 1998, IEEE Publications, 1998, pages 2491-2496, 1998. Keyword(s): input to state stability.


  2. X. Bao, Z. Lin, and E.D. Sontag. Some new results on finite gain $l_p$ stabilization of discrete-time linear systems subject to actuator saturation. In Proc. IEEE Conf. Decision and Control, Tampa, Dec. 1998, IEEE Publications, 1998, pages 4628-4629, 1998.


  3. B. Dasgupta and E.D. Sontag. A polynomial-time algorithm for an equivalence problem which arises in hybrid systems theory. In Proc. IEEE Conf. Decision and Control, Tampa, Dec. 1998, IEEE Publications, 1998, pages 1629-1634, 1998.


  4. M. Krichman and E.D. Sontag. A version of a converse Lyapunov theorem for input-output to state stability. In Proc. IEEE Conf. Decision and Control, Tampa, Dec. 1998, IEEE Publications, 1998, pages 4121-4126, 1998. Keyword(s): input to state stability.


  5. P. Kuusela, D. Ocone, and E.D. Sontag. On the VC dimension of continuous-time linear control systems. In Proc. 32nd Annual Conf. on Information Sciences and Systems (CISS 98), Princeton, NJ, pages 795-800, 1998.


  6. Y.S. Ledyaev and E.D. Sontag. Stabilization under measurement noise: Lyapunov characterization. In Proc. American Control Conf., Philadelphia, June 1998, pages 1658-166, 1998.


  7. D. Nesic and E.D. Sontag. Output stabilization of nonlinear systems: Linear systems with positive outputs as a case study. In Proc. IEEE Conf. Decision and Control, Tampa, Dec. 1998, IEEE Publications, 1998, pages 885-890, 1998.


  8. E.D. Sontag. Notions of integral input-to-state stability. In Proc. American Control Conf., Philadelphia, June 1998, pages 3215-321, 1998. Keyword(s): input to state stability.


  9. E.D. Sontag. Recent results on discontinuous stabilization and control-Lyapunov functions. In Proc. Workshop on Control of Nonlinear and Uncertain Systems, London, Feb. 1998, 1998. Keyword(s): control-Lyapunov functions.


  10. E.D. Sontag and Y. Qiao. Remarks on controllability of recurrent neural networks. In Proc. IEEE Conf. Decision and Control, Tampa, Dec. 1998, IEEE Publications, 1998, pages 501-506, 1998. Keyword(s): neural networks, recurrent neural networks.


1997
  1. F. Albertini and E.D. Sontag. Control-Lyapunov functions for time-varying set stabilization. In Proc. European Control Conf., Brussels, July 1997, 1997. Note: (Paper WE-E A5, CD-ROM file ECC515.pdf, 6 pages). Keyword(s): control-Lyapunov functions.


  2. Y.S. Ledyaev and E.D. Sontag. A remark on robust stabilization of general asymptotically controllable systems. In Proc. Conf. on Information Sciences and Systems (CISS 97), Johns Hopkins, Baltimore, MD, March 1997, pages 246-251, 1997. [PDF]
    Abstract:
    We showned in another recent paper that any asymptotically controllable system can be stabilized by means of a certain type of discontinuous feedback. The feedback laws constructed in that work are robust with respect to actuator errors as well as to perturbations of the system dynamics. A drawback, however, is that they may be highly sensitive to errors in the measurement of the state vector. This paper addresses this shortcoming, and shows how to design a dynamic hybrid stabilizing controller which, while preserving robustness to external perturbations and actuator error, is also robust with respect to measurement error. This new design relies upon a controller which incorporates an internal model of the system driven by the previously constructed feedback.


  3. E.D. Sontag. Some learning and systems-theoretic questions regarding recurrent neural networks. In Proc. Conf. on Information Sciences and Systems (CISS 97), Johns Hopkins, Baltimore, MD, March 1997, pages 630-635, 1997. Keyword(s): neural networks, VC dimension, recurrent neural networks.


  4. E.D. Sontag and Y. Wang. A notion of input to output stability. In Proc. European Control Conf., Brussels, July 1997, 1997. Note: (Paper WE-E A2, CD-ROM file ECC958.pdf, 6 pages). [PDF] Keyword(s): input to state stability, input to state stability.
    Abstract:
    This paper deals with a notion of "input to output stability (IOS)", which formalizes the idea that outputs depend in an "aymptotically stable" manner on inputs, while internal signals remain bounded. When the output equals the complete state, one recovers the property of input to state stability (ISS). When there are no inputs, one has a generalization of the classical concept of partial stability. The main results provide Lyapunov-function characterizations of IOS.


1996
  1. F.H. Clarke, Y.S. Ledyaev, E.D. Sontag, and A.I. Subbotin. Asymptotic controllability and feedback stabilization. In Proc. Conf. on Information Sciences and Systems (CISS 96)Princeton, NJ, pages 1232-1237, 1996. Keyword(s): control-Lyapunov functions, feedback stabilization.


  2. B. Dasgupta and E.D. Sontag. Sample complexity for learning recurrent perceptron mappings. In D.S. Touretzky, M.C. Moser, and M.E. Hasselmo, editors, Advances in Neural Information Processing Systems 8, pages 204-210, 1996. MIT Press, Cambridge, MA. Keyword(s): neural networks, VC dimension, recurrent neural networks.


  3. P. Koiran and E.D. Sontag. Neural networks with quadratic VC dimension. In D.S. Touretzky, M.C. Moser, and M.E. Hasselmo, editors, Advances in Neural Information Processing Systems 8, pages 197-203, 1996. MIT Press, Cambridge, MA. Keyword(s): neural networks, VC dimension.


  4. E.D. Sontag and Y. Wang. Detectability of nonlinear systems. In Proc. Conf. on Information Sciences and Systems (CISS 96), Princeton, NJ, pages 1031-1036, 1996. [PDF] Keyword(s): detectability, input to state stability.
    Abstract:
    Contains a proof of a technical step, which was omitted from the journal paper due to space constraints


1995
  1. E.D. Sontag. An abstract approach to dissipation. In Proc. IEEE Conf. Decision and Control, New Orleans, Dec. 1995, IEEE Publications, 1995, pages 2702-2703, 1995. Note: Full version, never submitted, is here: http://www.math.rutgers.edu/(tilde)sontag/FTPDIR/dissipation.pdf. [PDF]
    Abstract:
    We suggest that a very natural mathematical framework for the study of dissipation -in the sense of Willems, Moylan and Hill, and others- is that of indefinite quasimetric spaces. Several basic facts about dissipative systems are seen to be simple consequences of the properties of such spaces. Quasimetric spaces provide also one natural context for optimal control problems, and even for "gap" formulations of robustness.


  2. E.D. Sontag. Critical points for neural net least-squares problems. In Proc. 1995 IEEE Internat. Conf. Neural Networks, IEEE Publications, 1995, pages 2949-2954, 1995. Keyword(s): neural networks.


  3. E.D. Sontag. From linear to nonlinear: some complexity comparisons. In Proc. IEEE Conf. Decision and Control, New Orleans, Dec. 1995, IEEE Publications, 1995, pages 2916-2920, 1995. [PDF] Keyword(s): theory of computing and complexity, computational complexity, controllability, observability.
    Abstract:
    This paper deals with the computational complexity, and in some cases undecidability, of several problems in nonlinear control. The objective is to compare the theoretical difficulty of solving such problems to the corresponding problems for linear systems. In particular, the problem of null-controllability for systems with saturations (of a "neural network" type) is mentioned, as well as problems regarding piecewise linear (hybrid) systems. A comparison of accessibility, which can be checked fairly simply by Lie-algebraic methods, and controllability, which is at least NP-hard for bilinear systems, is carried out. Finally, some remarks are given on analog computation in this context.


  4. E.D. Sontag. Spaces of observables in nonlinear control. In Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994), Basel, pages 1532-1545, 1995. Birkhäuser. [PDF] Keyword(s): observability, dynamical systems.
    Abstract:
    Invited talk at the 1994 ICM. Paper deals with the notion of observables for nonlinear systems, and their role in realization theory, minimality, and several control and path planning questions.


  5. E.D. Sontag and H.J. Sussmann. Nonsmooth control-Lyapunov functions. In Proc. IEEE Conf. Decision and Control, New Orleans, Dec. 1995, IEEE Publications, 1995, pages 2799-2805, 1995. [PDF] Keyword(s): control-Lyapunov functions.
    Abstract:
    It is shown that the existence of a continuous control-Lyapunov function (CLF) is necessary and sufficient for null asymptotic controllability of nonlinear finite-dimensional control systems. The CLF condition is expressed in terms of a concept of generalized derivative (upper contingent derivative). This result generalizes to the non-smooth case the theorem of Artstein relating closed-loop feedback stabilization to smooth CLF's. It relies on viability theory as well as optimal control techniques. A "non-strict" version of the results, analogous to the LaSalle Invariance Principle, is also provided.


  6. E.D. Sontag and Y. Wang. On characterizations of input-to-state stability with respect to compact sets. In Proceedings of IFAC Non-Linear Control Systems Design Symposium, (NOLCOS '95), Tahoe City, CA, June 1995, pages 226-231, 1995. [PDF] Keyword(s): input to state stability.
    Abstract:
    Previous characterizations of ISS-stability are shown to generalize without change to the case of stability with respect to sets. Some results on ISS-stabilizability are mentioned as well.


  7. E.D. Sontag and Y. Wang. Various results concerning set input-to-state stability. In Proc. IEEE Conf. Decision and Control, New Orleans, Dec. 1995, IEEE Publications, 1995, pages 1330-1335, 1995. Keyword(s): input to state stability.


1994
  1. Y. Chitour, W. Liu, and E.D. Sontag. On the continuity and incremental gain properties of certain saturated linear feedback loops. In Proc. IEEE Conf. Decision and Control, Orlando, Dec. 1994, IEEE Publications, 1994, pages 127-132, 1994.


  2. B. DasGupta, H. T. Siegelmann, and E.D. Sontag. On a learnability question associated to neural networks with continuous activations (extended abstract). In COLT '94: Proceedings of the seventh annual conference on Computational learning theory, New York, NY, USA, pages 47-56, 1994. ACM Press. [doi:http://doi.acm.org/10.1145/180139.181009] Keyword(s): analog computing, neural networks, computational complexity, machine learning.


  3. R. Koplon and E.D. Sontag. Techniques for parameter reconstruction in Fourier-Neural recurrent networks. In Proc. IEEE Conf. Decision and Control, Orlando, Dec. 1994, IEEE Publications, 1994, pages 213-218, 1994. Keyword(s): neural networks, recurrent neural networks.


  4. Y. Lin and E.D. Sontag. On control-Lyapunov functions under input constraints. In Proc. IEEE Conf. Decision and Control, Orlando, Dec. 1994, IEEE Publications, 1994, pages 640-645, 1994. Keyword(s): control-Lyapunov functions.


  5. Y. Lin, E.D. Sontag, and Y. Wang. Recent results on Lyapunov-theoretic techniques for nonlinear stability. In Proc. Amer. Automatic Control Conf., Baltimore, June 1994, pages 1771-1775, 1994.


  6. E.D. Sontag and Y. Wang. Notions equivalent to input-to-state stability. In Proc. IEEE Conf. Decision and Control, Orlando, Dec. 1994, IEEE Publications, 1994, pages 3438-3443, 1994. Keyword(s): input to state stability.


  7. E.D. Sontag and Y. Wang. Orders of I/O equations and uniformly universal inputs. In Proc. IEEE Conf. Decision and Control, Orlando, Dec. 1994, IEEE Publications, 1994, pages 1270-1275, 1994. Keyword(s): identifiability, observability, realization theory.


1993
  1. F. Albertini and E.D. Sontag. Controllability of discrete-time nonlinear systems. In Systems and Networks: Mathematical Theory and Applications, Proc. MTNS '93, Vol. 2, Akad. Verlag, Regensburg, pages 35-38, 1993.


  2. F. Albertini and E.D. Sontag. Identifiability of discrete-time neural networks. In Proc. European Control Conf., Groningen, June 1993, pages 460-465, 1993. Keyword(s): neural networks, recurrent neural networks.


  3. F. Albertini and E.D. Sontag. State observability in recurrent neural networks. In Proc. IEEE Conf. Decision and Control, San Antonio, Dec. 1993, IEEE Publications, 1993, pages 3706-3707, 1993. Keyword(s): neural networks, observability, recurrent neural networks.


  4. F. Albertini and E.D. Sontag. Uniqueness of weights for recurrent nets. In Systems and Networks: Mathematical Theory and Applications, Proc. MTNS '93, Vol. 2, Akad. Verlag, Regensburg, pages 599-602, 1993. Note: Full version, never submitted for publication, is here: http://www.math.rutgers.edu/(tilde)sontag/FTPDIR/93mtns-nn-extended.pdf. [PDF] Keyword(s): neural networks, identifiability, recurrent neural networks.
    Abstract:
    This paper concerns recurrent networks x'=s(Ax+Bu), y=Cx, where s is a sigmoid, in both discrete time and continuous time. The paper establishes parameter identifiability under stronger assumptions on the activation than in "For neural networks, function determines form", but on the other hand deals with arbitrary (nonzero) initial states.


  5. J. L. Balcázar, R. Gavaldà, H. T. Siegelmann, and E.D. Sontag. Some structural complexity aspects of neural computation. In Proceedings of the Eighth Annual Structure in Complexity Theory Conference (San Diego, CA, 1993), Los Alamitos, CA, pages 253-265, 1993. IEEE Comput. Soc. Press. Keyword(s): analog computing, neural networks, computational complexity, super-Turing computation, theory of computing and complexity.


  6. C. Darken, M.J. Donahue, L. Gurvits, and E.D. Sontag. Rate of approximation results motivated by robust neural network learning. In COLT '93: Proceedings of the sixth annual conference on Computational learning theory, New York, NY, USA, pages 303-309, 1993. ACM Press. [doi:http://doi.acm.org/10.1145/168304.168357] Keyword(s): neural networks, optimization problems, approximation theory.


  7. R. Koplon and E.D. Sontag. Sign-linear systems as cascades of automata and continuous variable systems. In Proc. IEEE Conf. Decision and Control, San Antonio, Dec. 1993, IEEE Publications, 1993, pages 2290-2291, 1993.


  8. G.A. Lafferriere and E.D. Sontag. Remarks on control Lyapunov functions for discontinuous stabilizing feedback. In Proc. IEEE Conf. Decision and Control, San Antonio, Dec. 1993, IEEE Publications, 1993, pages 306-308, 1993. [PDF] Keyword(s): feedback stabilization.
    Abstract:
    We present a formula for a stabilizing feedback law under the assumption that a piecewise smooth control-Lyapunov function exists. The resulting feedback is continuous at the origin and smooth everywhere except on a hypersurface of codimension 1, assuming that certain transversality conditions are imposed there.


  9. Y. Lin, E.D. Sontag, and Y. Wang. Lyapunov-function characterizations of stability and stabilization for parameterized families of systems. In Proc. IEEE Conf. Decision and Control, San Antonio, Dec. 1993, IEEE Publications, 1993, pages 1978-1983, 1993.


  10. W. Liu, Y. Chitour, and E.D. Sontag. Remarks on finite gain stabilizability of linear systems subject to input saturation,. In Proc. IEEE Conf. Decision and Control, San Antonio, Dec. 1993, IEEE Publications, 1993, pages 1808-1813, 1993.


  11. A. Macintyre and E.D. Sontag. Finiteness results for sigmoidal neural networks. In STOC '93: Proceedings of the twenty-fifth annual ACM symposium on Theory of computing, New York, NY, USA, pages 325-334, 1993. ACM Press. [PDF] [doi:http://doi.acm.org/10.1145/167088.167192] Keyword(s): neural networks, theory of computing and complexity.
    Abstract:
    This paper deals with analog circuits. It establishes the finiteness of VC dimension, teaching dimension, and several other measures of sample complexity which arise in learning theory. It also shows that the equivalence of behaviors, and the loading problem, are effectively decidable, modulo a widely believed conjecture in number theory. The results, the first ones that are independent of weight size, apply when the gate function is the "standard sigmoid" commonly used in neural networks research. The proofs rely on very recent developments in the elementary theory of real numbers with exponentiation. (Some weaker conclusions are also given for more general analytic gate functions.) Applications to learnability of sparse polynomials are also mentioned.


  12. H.T. Siegelmann and E.D. Sontag. Analog computation via neural networks. In Proc. 2nd Israel Symposium on Theory of Computing and Systems (ISTCS93), IEEE Computer Society Press, 1993, 1993. Keyword(s): analog computing, neural networks, computational complexity, super-Turing computation, recurrent neural networks.


  13. E.D. Sontag. Numerical path planning based on nonsingular controls. In Proc. IEEE Conf. Decision and Control, San Antonio, Dec. 1993, IEEE Publications, 1993, pages 2706-2711, 1993.


  14. H.J. Sussmann, E.D. Sontag, and Y. Yang. A general result on the stabilization of linear systems using bounded controls. In Proc. IEEE Conf. Decision and Control, San Antonio, Dec. 1993, IEEE Publications, 1993, pages 1802-1807, 1993. Keyword(s): saturation.


  15. Y. Yang and E.D. Sontag. Stabilization with saturated actuators, a worked example: F-8 longitudinal flight control. In Proc. 1993 IEEE Conf. on Aerospace Control Systems, Thousand Oaks, CA, May 1993, pages 289-293, 1993. [PDF] Keyword(s): saturation.
    Abstract:
    This paper develops in detail an explicit design for control under saturation limits for the linearized equations of longitudinal flight control for an F-8 aircraft, and tests the obtained controller on the original nonlinear model.


1992
  1. F. Albertini and E.D. Sontag. For neural networks, function determines form. In Proc. IEEE Conf. Decision and Control, Tucson, Dec. 1992, IEEE Publications, 1992, pages 26-31, 1992. Keyword(s): neural networks, recurrent neural networks.


  2. M.A. Dahleh, E.D. Sontag, D.N.C. Tse, and J.N. Tsitsiklis. Worst-case identification of nonlinear fading memory systems. In Proc. Amer. Automatic Control Conf., Chicago, June 1992, pages 241-245, 1992.


  3. Y. Lin and E.D. Sontag. Gradient techniques for steering systems with no drift. In Proc. Conf. Inform. Sci. and Systems, Princeton University, March 1992, pages 1003-1008, 1992.


  4. R. Schwarzschild, E.D. Sontag, and M.L.J. Hautus. Output-Saturated Systems. In Proc. Amer. Automatic Control Conf. , Chicago, June 1992, pages 2504-2509, 1992.


  5. H.T. Siegelmann and E.D. Sontag. On the computational power of neural nets. In COLT '92: Proceedings of the fifth annual workshop on Computational learning theory, New York, NY, USA, pages 440-449, 1992. ACM Press. [doi:http://doi.acm.org/10.1145/130385.130432] Keyword(s): analog computing, neural networks, computational complexity, super-Turing computation, recurrent neural networks.


  6. H.T. Siegelmann and E.D. Sontag. Some results on computing with neural nets. In Proc. IEEE Conf. Decision and Control, Tucson, Dec. 1992, IEEE Publications, 1992, pages 1476-1481, 1992. Keyword(s): analog computing, neural networks, computational complexity, super-Turing computation, recurrent neural networks.


  7. H.T. Siegelmann, E.D. Sontag, and C.L. Giles. The Complexity of Language Recognition by Neural Networks. In Proceedings of the IFIP 12th World Computer Congress on Algorithms, Software, Architecture - Information Processing '92, Volume 1, pages 329-335, 1992. North-Holland. Keyword(s): neural networks, computational complexity, machine learning, recurrent neural networks, theory of computing and complexity.


  8. E.D. Sontag. Neural nets as systems models and controllers. In Proc. Seventh Yale Workshop on Adaptive and Learning Systems, Yale University, 1992, pages 73-79, 1992. [PDF] Keyword(s): neural networks, recurrent neural networks, neural networks.
    Abstract:
    A conference paper. Placed here because it was requested, but contains little that is not also contained in the survey on neural nets mentioned above.


  9. E.D. Sontag. Systems combining linearity and saturations, and relations to neural nets. In Nonlinear Control Systems Design 1992, IFAC Symposia Series, 1993, M. Fliess Ed., Pergamon Press, Oxford, 1993, pages 15-21, 1992. Note: (Also in Proc. Nonlinear Control Systems Design Symp., Bordeaux, June 1992, M. Fliess, Ed., IFAC Publications, pp. 242-247). Keyword(s): neural networks, recurrent neural networks.


  10. E.D. Sontag and Y. Lin. Stabilization with respect to noncompact sets: Lyapunov characterizations and effect of bounded inputs. In Nonlinear Control Systems Design 1992, IFAC Symposia Series, M. Fliess Ed., Pergamon Press, Oxford, 1993, pages 43-49, 1992. Note: Also in Proc. Nonlinear Control Systems Design Symp., Bordeaux, June 1992,(M. Fliess, Ed.), IFAC Publications, pp. 9--14. [PDF] Keyword(s): saturation.


  11. E.D. Sontag and Y. Wang. I/O equations in discrete and continuous time. In Proc. IEEE Conf. Decision and Control, Tucson, Dec. 1992, IEEE Publications, 1992, pages 3661-3662, 1992. Keyword(s): identifiability, observability, realization theory.


  12. Y. Yang, H.J. Sussmann, and E.D. Sontag. Stabilization of linear systems with bounded controls. In Nonlinear Control Systems Design 1992, IFAC Symposia Series, 1993, M. Fliess Ed., Pergamon Press, Oxford, 1993, pages 51-56, 1992. Note: Also in Proc. Nonlinear Control Systems Design Symp., Bordeaux, June 1992,(M. Fliess, Ed.), IFAC Publications, pp. 15-20.Keyword(s): saturation.


1991
  1. F. Albertini and E.D. Sontag. Accessibility of discrete-time nonlinear systems, and some relations to chaotic dynamics. In Proc. Conf. Inform. Sci. and Systems, John Hopkins University, March 1991, pages 731-736, 1991.


  2. F. Albertini and E.D. Sontag. Some connections between chaotic dynamical systems and control systems. In Proc. European Control Conf. , Vol 1, Grenoble, July 1991, pages 58-163, 1991. [PDF] Keyword(s): chaotic systems, controllability.
    Abstract:
    This paper shows how to extend recent results of Colonius and Kliemann, regarding connections between chaos and controllability, from continuous to discrete time. The extension is nontrivial because the results all rely on basic properties of the accessibility Lie algebra which fail to hold in discrete time. Thus, this paper first develops further results in nonlinear accessibility, and then shows how a theorem can be proved, which while analogous to the one given in the work by Colonius and Klieman, also exhibits some important differences. A counterexample is used to show that the theorem given in continuous time cannot be generalized in a straightforward manner.


  3. Y. Lin and E.D. Sontag. Further universal formulas for Lyapunov approaches to nonlinear stabilization. In Proc. Conf. Inform. Sci. and Systems, John Hopkins University, March 1991, pages 541-546, 1991.


  4. W. Maass, G. Schnitger, and E.D. Sontag. On the computational power of sigmoid versus Boolean threshold circuits (extended abstract). In Proceedings of the 32nd annual symposium on Foundations of computer science, Los Alamitos, CA, USA, pages 767-776, 1991. IEEE Computer Society Press. Keyword(s): neural networks, theory of computing and complexity.


  5. R. Schwarzschild and E.D. Sontag. Algebraic theory of sign-linear systems. In Proc. Amer. Automatic Control Conf., Boston, June 1991, pages 799-804, 1991.


  6. R. Schwarzschild and E.D. Sontag. Quantized systems, saturated measurements, and sign-linear systems. In Proc. Conf. Inform. Sci. and Systems, John Hopkins University, March 1991, pages 134-139, 1991. Keyword(s): observability.


  7. E.D. Sontag. Capabilities of four- vs three-layer nets, and control applications. In Proc. Conf. Inform. Sci. and Systems, John Hopkins University, March 1991, pages 558-563, 1991.


  8. E.D. Sontag. Feedback Stabilization Using Two-Hidden-Layer Nets. In Proc. Amer. Automatic Control Conf. , Boston, June 1991, pages 815-820, 1991.


  9. E.D. Sontag and Y. Wang. I/O equations for nonlinear systems and observation spaces. In Proc. IEEE Conf. Decision and Control, Brighton, UK, Dec. 1991, IEEE Publications, 1991, pages 720-725, 1991. [PDF] Keyword(s): identifiability, observability, realization theory.
    Abstract:
    This paper studies various types of input/output representations for nonlinear continuous time systems. The algebraic and analytic i/o equations studied in previous papers by the authors are generalized to integral and integro-differential equations, and an abstract notion is also considered. New results are given on generic observability, and these results are then applied to give conditions under which that the minimal order of an equation equals the minimal possible dimension of a realization, just as with linear systems but in contrast to the discrete time nonlinear theory.


1990
  1. T. Asano, J. Hershberger, J. Pach, E.D. Sontag, D. Souivaine, and S. Suri. Separating bi-chromatic points by parallel lines. In Proceedings of the Second Canadian Conf. on Computational Geometry, Ottawa, Canada, 1990, pages 46-49, 1990. [PDF] Keyword(s): computational geometry.
    Abstract:
    Given a 2-coloring of the vertices of a regular n-gon P, how many parallel lines are needed to separate the vertices into monochromatic subsets? We prove that floor(n/2) is a tight upper bound, and also provide an O(n log n) time algorithm to determine the direction that gives the minimum number of lines. If the polygon is a non-regular convex polygon, then n-3 lines may be necessary, while n-2 lines always suffice. This problem arises in machine learning and has implications about the representational capabilities of some neural networks.


  2. H. Dewan and E.D. Sontag. Extrapolatory methods for speeding up the BP algorithm. In Proc. Int. Joint Conf. on Neural Networks, Washington, DC, Jan. 1990, IEEE Publications, 1990, pages I.613-616, 1990. Keyword(s): neural networks.


  3. E.D. Sontag. Comparing sigmoids and heavisides. In Proc. Conf. Info. Sci. and Systems, Princeton, 1990, pages 654-659, 1990. Keyword(s): neural networks, boolean systems.


  4. E.D. Sontag. Remarks on interpolation and recognition using neural nets. In NIPS-3: Proceedings of the 1990 conference on Advances in neural information processing systems 3, San Francisco, CA, USA, pages 939-945, 1990. Morgan Kaufmann Publishers Inc.. Keyword(s): neural networks.


  5. E.D. Sontag and H.J. Sussmann. Nonlinear output feedback design for linear systems with saturating controls. In Proc. IEEE Conf. Decision and Control, Honolulu, Dec. 1990, IEEE Publications, 1990, pages 3414-3416, 1990. [PDF] Keyword(s): saturation.
    Abstract:
    This paper shows the existence of (nonlinear) smooth dynamic feedback stabilizers for linear time invariant systems under input constraints, assuming only that open-loop asymptotic controllability and detectability hold.


  6. Y. Wang and E.D. Sontag. Realization of families of generating series: differential algebraic and state space equations. In Proc. 11th IFAC World Congress, Tallinn, former USSR, 1990, pages 62-66, 1990. Keyword(s): identifiability, observability, realization theory.


1989
  1. E.D. Sontag. Remarks on stabilization and input-to-state stability. In Proceedings of the 28th IEEE Conference on Decision and Control, Vol. 1--3 (Tampa, FL, 1989), New York, pages 1376-1378, 1989. IEEE. [PDF] Keyword(s): input to state stability.
    Abstract:
    This paper describes how notions of input-to-state stabilization are useful when stabilizing cascades of systems. The simplest result along these lines is local, and it states that a cascade of two locally asymptotically stable systems is again asystable. A global result is obtained if both systems have the origin as a globally asymptotically stable state and the "converging input bounded state" property holds for the second system. Relations to input to state stability and the "bounded input bounded state" property as mentioned as well.


  2. E.D. Sontag. Remarks on the time-optimal control of a class of Hamiltonian systems. In Proceedings of the 28th IEEE Conference on Decision and Control, Vol. 1--3 (Tampa, FL, 1989), New York, pages 217-221, 1989. IEEE. [PDF] Keyword(s): robotics, optimal control.
    Abstract:
    This paper introduces a subclass of Hamiltonian control systems motivated by mechanical models. It deals with time-optimal control problems. The main results characterize regions of the state space where singular trajectories cannot exist, and provide high-order conditions for optimality.


  3. E.D. Sontag. Some connections between stabilization and factorization. In Proceedings of the 28th IEEE Conference on Decision and Control, Vol. 1--3 (Tampa, FL, 1989), New York, pages 990-995, 1989. IEEE. [PDF]
    Abstract:
    Coprime right fraction representations are obtained for nonlinear systems defined by differential equations, under assumptions of stabilizability and detectability. A result is also given on left (not necessarily coprime) factorizations.


  4. E.D. Sontag. Some recent results on nonlinear feedback. In Proc. Conf. Info. Sciences and Systems, Johns Hopkins University Press, 1989, pages 151-156, 1989.


  5. E.D. Sontag and H.J. Sussmann. Backpropagation Separates when Perceptrons Do. In Proc. IEEE Int. Conf. Neural Networks, Washington, DC, June 1989, pages 639-642, 1989.


  6. E.D. Sontag and H.J. Sussmann. Remarks on local minima in backpropagation. In Proc. Conf. Info. Sciences and Systems, Johns Hopkins University Press, 1989, pages 432-435, 1989. Keyword(s): neural networks.


  7. Y. Wang and E.D. Sontag. A new result on the relation between differential-algebraic realizability and state space realizations. In Proc. Conf. Info. Sciences and Systems, Johns Hopkins University Press, 1989, pages 143-147, 1989. Keyword(s): identifiability, observability, realization theory.


  8. Y. Wang and E.D. Sontag. Realization and input/output relations: the analytic case. In Proceedings of the 28th IEEE Conference on Decision and Control, Vol. 1--3 (Tampa, FL, 1989), New York, pages 1975-1980, 1989. IEEE. Keyword(s): identifiability, observability, realization theory.


1988
  1. E.D. Sontag. Some complexity questions regarding controllability. In Proc. IEEE Conf. Decision and Control, Austin, Dec. 1988, pages 1326-1329, 1988. [PDF] Keyword(s): theory of computing and complexity, computational complexity, controllability, computational complexity.
    Abstract:
    It has been known for a long time that certain controllability properties are more difficult to verify than others. This article makes this fact precise, comparing controllability with accessibility, for a wide class of nonlinear continuous time systems. The original contribution is in formalizing this comparison in the context of computational complexity. (This paper placed here by special request.)


  2. E.D. Sontag. Stabilizability, i/o stability, and coprime factorizations. In Proc. IEEE Conf. Decision and Control, Austin, Dec. 1988, pages 457-458, 1988. Keyword(s): input to state stability.


1987
  1. B. Jakubczyk and E.D. Sontag. The effect of sampling on feedback linearization. In Proc. IEEE Conf. Decision and Control, Los Angeles, Dec.1987, pages 1374-1379, 1987.


  2. E.D. Sontag. An approach to the automatic design of first-order controllers along reference trajectories. In Proc. IEEE Conf. Decision and Control, Los Angeles, Dec.1987, pages 363-1367, 1987.


  3. E.D. Sontag. Equilinearization: A simplified derivation and experimental results. In Proc. Conf. Info. Sciences and Systems, Johns Hopkins University Press, pages 490-495, 1987.


1986
  1. E.D. Sontag. Controllability and linearized regulation. In Proc. Conf. Info. Sci. and Systems, Princeton, 1986, pages 67-671, 1986.


  2. E.D. Sontag and H.J. Sussmann. Time-optimal control of manipulators. In Proc. IEEE Int.Conf.on Robotics and Automation, San Francisco, April 1986, pages 1692-1697, 1986. [PDF] Keyword(s): robotics, optimal control.
    Abstract:
    This paper studies time-optimal control questions for a certain class of nonlinear systems. This class includes a large number of mechanical systems, in particular, rigid robotic manipulators with torque constraints. As nonlinear systems, these systems have many properties that are false for generic systems of the same dimensions.


1985
  1. E.D. Sontag. Further results on accessibility under sampling. In Proc.Conf. Info. Sci. and Systems, Johns Hopkins University, March 1985, 1985.


  2. E.D. Sontag and H.J. Sussmann. Image restoration and segmentation using the annealing algorithm. In Proc. IEEE Conf. Dec. and Control, 1985, pages 768-773, 1985. [PDF] Keyword(s): image processing, optimization.
    Abstract:
    We consider the problem of estimating a signal, which is known -- or assumed -- to be constant on each of the members of a partition of a square lattice into m unknown regions, from the observation of the signal plus Gaussian noise. This is a nonlinear estimation problem, for which it is not appropriate to use the conditional expectation as the estimate. We show that, at least in principle, the "maximum iikelihood estimator" (MLE) proposed by Geman and Geman lends itself to numerical computation using the annealing algorithm. We argue that the MLE by itself can be, under certain conditions (low signal to noise ratio), a very unsatisfactory estimator, in that it does worse than just deciding that the signal was zero. However, if combined with a rule which we propose, for deciding when to use and when to ignore it, the MLE can provide a reasonable suboptimal estimator. We then discuss preliminary numerical data obtained using the annealing method. These results indicate that: (a) the annealing algorithm performs remarkably well, and (b) a criterion can be formulated in terms of quantities computed from the observed image (without using a priori knowledge of the signal-to-noise ratio) for deciding when to keep the MLE.


  3. E.D. Sontag and H.J. Sussmann. Remarks on the time-optimal control of two-link manipulators. In Proc. IEEE Conf. Dec. and Control, 1985, pages 1646-1652, 1985. [PDF] Keyword(s): optimal control, robotics.


1984
  1. E.D. Sontag. Remarks on input/output linearization. In Proc. IEEE Conf. Dec. and Control, Las Vegas, Dec. 1984, pages 409-412, 1984. [PDF]
    Abstract:
    In the context of realization theory, conditions are given for the possibility of simulating a given discrete time system, using immersion and/or feedback, by linear or state-affine systems.


1983
  1. E.D. Sontag. Further remarks preservation of accessibility under sampling. In Proc. Johns Hopkins Conf. on Info. Sci. and Systems, 1983, pages 326-332, 1983.


1982
  1. E.D. Sontag. Abstract regulation of nonlinear systems: Stabilization, Part II. In Proc.Princeton Conf.on Information Sciences and Systems, Princeton, March 1982, pages 431-435, 1982. Keyword(s): feedback stabilization.


  2. E.D. Sontag. Small-input controllability. In Proc. IEEE Conf. Dec. and Control, Orlando, Dec. 1982, 1982.


  3. E.D. Sontag and H.J. Sussmann. Accessibility under sampling. In Proc. IEEE Conf. Dec. and Control, Orlando, Dec. 1982, 1982. [PDF] Keyword(s): discrete-time.
    Abstract:
    This note addresses the following problem: Find conditions under which a continuous-time (nonlinear) system gives rise, under constant rate sampling, to a discrete-time system which satisfies the accessibility property.


1981
  1. P.P. Khargonekar and E.D. Sontag. On the relation between stable matrix fraction decompositions and regulable realizations of systems over rings. In Proc. IEEE Conf.Dec. and Control, San Diego, Dec. 1981, pages 1006-1011, 1981. Keyword(s): systems over rings.


1980
  1. E.D. Sontag. Nonlinear regulation, the piecewise linear approach. In Proc.Princeton Conf.on Information Sciences and Systems, Princeton, March 1980, 1980. Keyword(s): piecewise linear systems.


  2. E.D. Sontag and H.J. Sussmann. Remarks on continuous feedback. In Proc. IEEE Conf. Decision and Control, Albuquerque, Dec.1980, pages 916-921, 1980. [PDF] Keyword(s): feedback stabilization.
    Abstract:
    We show that, in general, it is impossible to stabilize a controllable system by means of a continuous feedback, even if memory is allowed. No optimality considerations are involved. All state spaces are Euclidean spaces, so no obstructions arising from the state space topology are involved either. For one dimensional state and input, we prove that continuous stabilization with memory is always possible. (This is an old conference paper, never published in journal form but widely cited nonetheless. Warning: file is very large, since it was scanned.)


1978
  1. E.D. Sontag. Algebraic-geometric methods in the realization of discrete-time systems. In Proc. Conf. Inform. Sci. and Systems, John Hopkins Univ. (1978), pages 158-162, 1978.



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