1. E.D. Sontag. Mathematical Control Theory. Deterministic Finite-Dimensional Systems, volume 6 of Texts in Applied Mathematics. Springer-Verlag, New York, 1990. Abstract:

   The second edition (1998) is now online; please follow that link.

1. E.D. Sontag. Constant McMillan degree and the continuous stabilization of families of transfer matrices. In Control of uncertain systems (Bremen, 1989), volume 6 of Progr. Systems Control Theory, pages 289-295. Birkhäuser Boston, Boston, MA, 1990. [PDF] Keyword(s): systems over rings, parametric classes of systems.



2. E.D. Sontag. Feedback stabilization of nonlinear systems. In Robust control of linear systems and nonlinear control (Amsterdam, 1989), volume 4 of Progr. Systems Control Theory, pages 61-81. Birkhäuser Boston, Boston, MA, 1990. [PDF] Abstract:

   This paper surveys some well-known facts as well as some recent developments on the topic of stabilization of nonlinear systems. (NOTE: figures are not included in file; they were pasted-in.)




3. E.D. Sontag. Integrability of certain distributions associated with actions on manifolds and applications to control problems. In Nonlinear controllability and optimal control, volume 133 of Monogr. Textbooks Pure Appl. Math., pages 81-131. Dekker, New York, 1990. [PDF] Keyword(s): controllability. Abstract:

   Results are given on the integrability of certain distributions which arise from smoothly parametrized families of diffeomorphisms acting on manifolds. Applications to control problems and in particular to the problem of sampling are discussed. Pages 42-50 apply the results to the control of continuous time systems; this is an exposition of some of the basic results of the Lie algebraic accessibility theory.




4. E.D. Sontag and Y. Wang. Input/output equations and realizability. In Realization and modelling in system theory (Amsterdam, 1989), volume 3 of Progr. Systems Control Theory, pages 125-132. Birkhäuser Boston, Boston, MA, 1990. [PDF] Keyword(s): identifiability, observability, realization theory.



5. B. Jakubczyk and E.D. Sontag. Controllability of nonlinear discrete-time systems: a Lie-algebraic approach. SIAM J. Control Optim., 28(1):1-33, 1990. [PDF] [doi:http://dx.doi.org/10.1137/0328001] Keyword(s): discrete-time. Abstract:

   This paper presents a geometric study of controllability for discrete-time nonlinear systems. Various accessibility properties are characterized in terms of Lie algebras of vector fields. Some of the results obtained are parallel to analogous ones in continuous-time, but in many respects the theory is substantially different and many new phenomena appear.




6. E.D. Sontag. Further facts about input to state stabilization. IEEE Trans. Automat. Control, 35(4):473-476, 1990. [PDF] Keyword(s): input to state stability, ISS, stabilization. Abstract:

   Previous results about input to state stabilizability are shown to hold even for systems which are not linear in controls, provided that a more general type of feedback be allowed. Applications to certain stabilization problems and coprime factorizations, as well as comparisons to other results on input to state stability, are also briefly discussed.d local minima may occur, if the data are not separable and sigmoids are used.




7. E.D. Sontag and Y. Wang. Pole shifting for families of linear systems depending on at most three parameters. Linear Algebra Appl., 137/138:3-38, 1990. [PDF] Keyword(s): systems over rings, systems over rings, parametric classes of systems. Abstract:

   We prove that for any family of n-dimensional controllable linear systems, continuously parameterized by up to three parameters, and for any continuous selection of n eigenvalues (in complex conjugate pairs), there is some dynamic controller of dimension 3n which is itself continuously parameterized and for which the closed-loop eigenvalues are these same eigenvalues, each counted 4 times. An analogous result holds also for smooth parameterizations.

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, Lawrence Erlbaum Associates, Inc., Publishers, ISBN 0-8058-0775-6, pages I.613-616, 1990. [PDF] Keyword(s): machine learning, neural networks. Abstract:

   We describe a speedup technique that uses extrapolatory methods to predict the weights in a Neural Network using Back Propagation (BP) learning. The method is based on empirical observations of the way the weights change as a function of time. We use numerical function fitting techniques to determine the parameters of an extrapolation function and then use this function to project weights into the future. Significant computational savings result by using the extrapolated weights to jump over many iterations of the standard algorithm, achieving comparable performance with fewer iterations.




3. E.D. Sontag. Comparing sigmoids and heavisides. In Proc. Conf. Info. Sci. and Systems, Princeton, 1990, pages 654-659, 1990. Keyword(s): machine learning, 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): machine learning, 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, bounded inputs. 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.

1. F. Albertini and E.D. Sontag. Some connections between chaotic dynamical systems and control systems. Technical report SYCON-90-13, Rutgers Center for Systems and Control, 1990.

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