STATE SPACE NEURAL NETWORKS IN NON-LINEAR ADAPTIVE SYSTEM IDENTIFICATION AND CONTROL

Non-linear control design methods, such as feedback linearisation and output regulation theory, are effective techniques for solving non-linear control problems. However, they assume the exact knowledge of the true model and that the states are completely accessible, which is not always true in practice. The starting point for this paper is to develop a viable practical control strategy by combining the modelling capabilities of state space neural networks with the effectiveness of the output regulation theory. By using input and output measurements and based on Lyapunov stability and non-linear observation theories a stable on-line learning methodology for the network parameters is proposed. A practical implementation for controlling a multivariable process is included to illustrate the effectiveness of the proposed adaptive control methodology.

[1]  Michel Verhaegen,et al.  Adaptive output tracking of nonlinear systems using neural networks , 1999 .

[2]  K. S. Narendra,et al.  Neural networks for control theory and practice , 1996, Proc. IEEE.

[3]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[4]  D. Luenberger An introduction to observers , 1971 .

[5]  Paul J. Werbos,et al.  Backpropagation Through Time: What It Does and How to Do It , 1990, Proc. IEEE.

[6]  B. Francis The linear multivariable regulator problem , 1976, 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes.

[7]  M. Agarwal A systematic classification of neural-network-based control , 1997 .

[8]  A. Isidori,et al.  Output regulation of nonlinear systems , 1990 .

[9]  F. Thau Observing the state of non-linear dynamic systems† , 1973 .

[10]  D. Normand-Cyrot,et al.  Minimum-phase nonlinear discrete-time systems and feedback stabilization , 1987, 26th IEEE Conference on Decision and Control.

[11]  Ah Chung Tsoi,et al.  Discrete time recurrent neural network architectures: A unifying review , 1997, Neurocomputing.

[12]  J. Henriques,et al.  A recurrent neuronal approach for the nonlinear discrete time output regulation , 2000, 2000 26th Annual Conference of the IEEE Industrial Electronics Society. IECON 2000. 2000 IEEE International Conference on Industrial Electronics, Control and Instrumentation. 21st Century Technologies.

[13]  Madan M. Gupta,et al.  Dynamic recurrent neural networks for approximation of nonlinear systems , 1999 .

[14]  Graham Goodwin,et al.  Discrete time multivariable adaptive control , 1979, 1979 18th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[15]  Ronald J. Williams,et al.  Gradient-based learning algorithms for recurrent networks and their computational complexity , 1995 .

[16]  Johan A. K. Suykens,et al.  NLq Theory: A Neural Control Framework with Global Asymptotic Stability Criteria , 1997, Neural Networks.

[17]  Mietek A. Brdys,et al.  Stable adaptive control with recurrent networks , 1997, 1997 European Control Conference (ECC).

[18]  Jie Huang,et al.  Stabilization on zero-error manifolds and the nonlinear servomechanism problem , 1990, 29th IEEE Conference on Decision and Control.

[19]  Manolis A. Christodoulou,et al.  Neural adaptive regulation of unknown nonlinear dynamical systems , 1997, IEEE Trans. Syst. Man Cybern. Part B.

[20]  E. A. Misawa,et al.  A Study on Sliding Mode State Estimation , 1999 .

[21]  Kenneth J. Hunt,et al.  Applications of Neural Adaptive Control Technology , 1997 .

[22]  Kumpati S. Narendra,et al.  Gradient methods for the optimization of dynamical systems containing neural networks , 1991, IEEE Trans. Neural Networks.