Laboratory for Control, Learning, and Systems Biology

1992

  1. ▪F. Albertini, E.D. Sontag, "For neural networks, function determines form", In Proc.\ IEEE Conf.\ Decision and Control, Tucson, Dec.\ 1992, IEEE Publications, 1992, pp. 26–31, 1992.
    machine learning · artificial intelligence · neural networks · recurrent neural networks
  2. ▪M.A. Dahleh, E.D. Sontag, D.N.C. Tse, J.N. Tsitsiklis, "Worst-case identification of nonlinear fading memory systems", In Proc.\ Amer.\ Automatic Control Conf., Chicago, June 1992, pp. 241–245, 1992. pdf
    information-based complexity · fading-memory systems · stability · system identification · structured uncertainty · identifiability
    Abstract

    Preliminary version of paper published in Automatica in 1995.

  3. ▪Y. Lin, E.D. Sontag, "Gradient techniques for steering systems with no drift", In Proc.\ Conf.\ Inform.\ Sci.\ and Systems, Princeton University, March 1992, pp. 1003–1008, 1992.
  4. ▪R. Schwarzschild, E.D. Sontag, M.L.J. Hautus, "Output-Saturated Systems", In Proc.\ Amer.\ Automatic Control Conf.\ \/, Chicago, June 1992, pp. 2504–2509, 1992.
  5. ▪H.T. Siegelmann, E.D. Sontag, 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, pp. 329–335, 1992.
    machine learning · artificial intelligence · neural networks · computational complexity · machine learning · recurrent neural networks · theory of computing and complexity
  6. ▪H.T. Siegelmann, E.D. Sontag, "On the computational power of neural nets", In COLT '92: Proceedings of the fifth annual workshop on Computational learning theory, pp. 440–449, 1992. doi
    machine learning · artificial intelligence · analog computing · neural networks · computational complexity · super-Turing computation · recurrent neural networks
  7. ▪H.T. Siegelmann, E.D. Sontag, "Some results on computing with neural nets", In Proc.\ IEEE Conf.\ Decision and Control, Tucson, Dec.\ 1992, IEEE Publications, 1992, pp. 1476–1481, 1992.
    machine learning · artificial intelligence · analog computing · neural networks · computational complexity · super-Turing computation · recurrent neural networks
  8. ▪E.D. Sontag, "Universal nonsingular controls", Systems Control Lett., vol. 19, no. 3, pp. 221–224, 1992. doipdf
    Erratum appeared in SCL 20(1993), p. 77, can be found in same file.
    controllability · real-analytic functions
    Abstract

    For analytic systems satisfying the strong accessibility rank condition, generic inputs produce trajectories along which the linearized system is controllable. Applications to the steering of systems without drift are briefly mentioned.

  9. ▪E.D. Sontag, "Feedback stabilization using two-hidden-layer nets", IEEE Trans.\ Neural Networks, vol. 3, pp. 981–990, 1992. pdf
    machine learning · artificial intelligence · neural networks · feedback stabilization
    Abstract

    This paper compares the representational capabilities of one hidden layer and two hidden layer nets consisting of feedforward interconnections of linear threshold units. It is remarked that for certain problems two hidden layers are required, contrary to what might be in principle expected from the known approximation theorems. The differences are not based on numerical accuracy or number of units needed, nor on capabilities for feature extraction, but rather on a much more basic classification into "direct" and "inverse" problems. The former correspond to the approximation of continuous functions, while the latter are concerned with approximating one-sided inverses of continuous functions - and are often encountered in the context of inverse kinematics determination or in control questions. A general result is given showing that nonlinear control systems can be stabilized using two hidden layers, but not in general using just one.

  10. ▪E.D. Sontag, "Feedforward nets for interpolation and classification", J. Comput. System Sci., vol. 45, no. 1, pp. 20–48, 1992. doipdf
    machine learning · artificial intelligence · neural networks · VC dimension · boolean systems
    Abstract

    This paper deals with single-hidden-layer feedforward nets, studying various aspects of classification power and interpolation capability. In particular, a worst-case analysis shows that direct input to output connections in threshold nets double the recognition but not the interpolation power, while using sigmoids rather than thresholds allows doubling both. For other measures of classification, including the Vapnik-Chervonenkis dimension, the effect of direct connections or sigmoidal activations is studied in the special case of two-dimensional inputs.

  11. ▪E.D. Sontag, "Neural nets as systems models and controllers", In Proc.\ Seventh Yale Workshop on Adaptive and Learning Systems\/, Yale University, 1992, pp. 73–79, 1992. pdf
    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.

  12. ▪E.D. Sontag, 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, pp. 43–49, 1992. pdf
    Also in Proc.\ Nonlinear Control Systems Design Symp., Bordeaux, June 1992,(M.\ Fliess, Ed.), IFAC Publications, pp. 9–14
    saturation · bounded inputs
  13. ▪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, pp. 15–21, 1992.
    (Also in Proc.\ Nonlinear Control Systems Design Symp., Bordeaux, June 1992, M.\ Fliess, Ed., IFAC Publications, pp. 242-247)
    machine learning · artificial intelligence · neural networks · recurrent neural networks
  14. ▪E.D. Sontag, Y. Wang, "I/O equations in discrete and continuous time", In Proc.\ IEEE Conf.\ Decision and Control, Tucson, Dec.\ 1992, IEEE Publications, 1992, pp. 3661–3662, 1992.
    identifiability · observability · realization theory
  15. ▪Y. Wang, E.D. Sontag, "Generating series and nonlinear systems: analytic aspects, local realizability, and i/o representations", Forum Math., vol. 4, no. 3, pp. 299–322, 1992. pdf
    identifiability · observability · realization theory · input/output system representations · real-analytic functions
    Abstract

    This paper studies fundamental analytic properties of generating series for nonlinear control systems, and of the operators they define. It then applies the results obtained to the extension of facts, which relate realizability and algebraic input/output equations, to local realizability and analytic equations.

  16. ▪Y. Wang, E.D. Sontag, "Algebraic differential equations and rational control systems", SIAM J. Control Optim., vol. 30, no. 5, pp. 1126–1149, 1992. pdf
    identifiability · observability · realization theory · input/output system representations
    Abstract

    It is shown that realizability of an input/output operators by a finite-dimensional continuous-time rational control system is equivalent to the existence of a high-order algebraic differential equation satisfied by the corresponding input/output pairs ("behavior"). This generalizes, to nonlinear systems, the classical equivalence between autoregressive representations and finite dimensional linear realizability.

  17. ▪Y. Yang, H.J. Sussmann, 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, pp. 51–56, 1992.
    Also in Proc.\ Nonlinear Control Systems Design Symp., Bordeaux, June 1992,(M.\ Fliess, Ed.), IFAC Publications, pp. 15-20.
    saturation · bounded inputs