Recursive identification using feedforward neural networks

The paper is concerned with the identification of an unknown nonlinear dynamical system when only the inputs and outputs are accessible for measurement. Under certain assumptions it is shown that, generically, the system can be realized by a recursive input-output model. Furthermore, relying on the approximation properties of neural networks and the existence of effective training algorithms, it is demonstrated how an effective identification model can be constructed. Simulation results are presented to complement the theoretical discussions.

[1]  M. Reed Methods of Modern Mathematical Physics. I: Functional Analysis , 1972 .

[2]  M. Golubitsky,et al.  Stable mappings and their singularities , 1973 .

[3]  Lennart Ljung,et al.  Analysis of recursive stochastic algorithms , 1977 .

[4]  Eduardo Sontag Polynomial Response Maps , 1979 .

[5]  D. Aeyels GENERIC OBSERVABILITY OF DIFFERENTIABLE SYSTEMS , 1981 .

[6]  W. Rugh Nonlinear System Theory: The Volterra / Wiener Approach , 1981 .

[7]  I. J. Leontaritis,et al.  Input-output parametric models for non-linear systems Part II: stochastic non-linear systems , 1985 .

[8]  Geoffrey E. Hinton,et al.  Learning internal representations by error propagation , 1986 .

[9]  Kurt Hornik,et al.  Multilayer feedforward networks are universal approximators , 1989, Neural Networks.

[10]  Kumpati S. Narendra,et al.  Identification and control of dynamical systems using neural networks , 1990, IEEE Trans. Neural Networks.

[11]  Eduardo Sontag,et al.  Controllability of Nonlinear Discrete-Time Systems: A Lie-Algebraic Approach , 1990, SIAM Journal on Control and Optimization.

[12]  Michael I. Jordan Attractor dynamics and parallelism in a connectionist sequential machine , 1990 .

[13]  George Cybenko,et al.  Approximation by superpositions of a sigmoidal function , 1992, Math. Control. Signals Syst..

[14]  A. U. Levin,et al.  Neural networks in dynamical systems: a system theoretic approach , 1992 .

[15]  K S Narendra,et al.  Control of nonlinear dynamical systems using neural networks. II. Observability, identification, and control , 1996, IEEE Trans. Neural Networks.