Abstract
Several empirical studies have demonstrated the feasibility of employing neural networks as models of nonlinear dynamical systems. This paper presents a stability theory approach to synthesizing and analyzing neural network based identification schemes. First static network architectures are combined with dynamical elements in the form of stable filters to construct a type of recurrent network configuration which is shown to be capable of approximating a large class of dynamical systems. Identification schemes, based on neural network models, are then developed using the Lyapunov synthesis approach with the projection modification method. These identification schemes are shown to guarantee stability of the overall system, even in the presence of modeling errors.
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References
L. Ljung, System Identification: Theory for the User, Englewood Cliffs, NJ, Prentice-Hall, 1987.
G.C. Goodwin and K.S. Sin, Adaptive Filtering Prediction and Control, Englewood Cliffs, NJ, Prentice-Hall, 1984.
K.S. Narendra and A.M. Annaswamy, Stable Adaptive Systems, Englewood Cliffs, NJ, Prentice-Hall, 1989.
S.A. Billings, “Identification of Nonlinear Systems—a survey”, IEE Proceedings, vol. 127, pt. D, no. 6, Nov. 1980.
K.S. Narendra and K. Parthasarathy, “Identification and control of dynamical systems using neural networks”, IEEE Trans. on Neural Networks, vol. 1, pp.4–2’7, 1990.
M.I. Jordan and D.E. Rumelhart “Forward models: supervised learning with a distal teacher”, Occ. Paper #.¢0,Center for Cognitive Science, M.I.T., 1990.
A.G. Barto, “Connectionist learning for control: an overview”, in Neural Networks for Control, T.W. Miller, R.S. Sutton III, and P.J. Werbos, Eds, pp. 5–58, Cambridge, MA, The MIT Press, 1990.
G. Cybenko, “Approximation by superpositions of a sigmoidal function”, Mathematics of Control, Signals, and Systems, vol. 2, pp. 303–314, 1989.
K. Hornik, M. Stinchcombe, and H. White, “Multilayer feedforward networks are universal approximators”, Neural Networks, vol. 2, pp. 359–366, 1989.
E.J. Hartman, J.D. Keeler, and J.M. Kowalski, “Layered neural networks with guassian hidden units as universal approximations”, Neural Computation, vol. 2, pp. 210–215, 1990.
J. Park and I.W. Sandberg, “Universal approximation using radial-basisfunction networks”, Neural Computation, vol. 3, pp. 246–257, 1991.
P.C. Parks, “Lyapunov redesign of model reference adaptive control systems”, IEEE Trans. Aut. Control, vol. AC-11, pp. 362–367, 1966.
P.A. Ioannou and A. Datta, “Robust Adaptive Control: Design, Analysis and Robustness Bounds”, in Foundations of Adaptive Control, P.V. Kokotovic ed., pp. 71–152, Springer-Verlag, Berlin, 1991.
G.C. Goodwin and D.Q. Mayne, “A parameter estimation perspective of continuous time model reference adaptive control”, Automaiica, vol. 23, pp. 57–70, Jan. 1987.
M.M. Polycarpou and P.A. Ioannou “Identification and Control of Nonlinear Systems Using Neural Network Models: Design and Stability Analysis”, Tech. Rep. No. 91–09–01, Dept. Elec. Eng. - Systems, Univ. of Southern Cal., Sept. 1991.
D.E. Rumelhart, J.L. McClelland and the PDP Research group, Parallel Distributed Processing: Exploration in the Microstructure of Cognition. Volume 1: Foundations, Cambridge, MA, The MIT Press, 1986.
J.K. Hale, Ordinary Differential Equations, New York, NY, WileyInterScience, 1969.
P.A. Ioannou and P.V. Kokotovic, Adaptive Systems with Reduced Models, Springer-Verlag, New York, NY, 1983.
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Polycarpou, M.M., Ioannou, P.A. (1993). Stable Nonlinear System Identification Using Neural Network Models. In: Bekey, G.A., Goldberg, K.Y. (eds) Neural Networks in Robotics. The Springer International Series in Engineering and Computer Science, vol 202. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-3180-7_9
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DOI: https://doi.org/10.1007/978-1-4615-3180-7_9
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