Adaptive control of nonlinear multivariable systems using neural networks

In this paper we examine the problem of control of multivariable systems using neural networks. The problem is discussed assuming different amounts of prior information concerning the plant and hence different levels of complexity. In the first stage it is assumed that the state equations describing the plant are known and that the state of the system is accessible. Following this the same problem is considered when the state equations are unknown. In the last stage the adaptive control of the multivariable system using only input-output data is discussed in detail. The objective of the paper is to demonstrate that results from nonlinear control theory and linear adaptive control theory can be used to design practically viable controllers for unknown nonlinear multivariable systems using neural networks. The different assumptions that have to be made, the choice of identifier and controller architectures and the generation of adaptive laws for the adjustment of the parameters of the neural networks form the core of the paper.<<ETX>>

[1]  Andrew R. Barron,et al.  Universal approximation bounds for superpositions of a sigmoidal function , 1993, IEEE Trans. Inf. Theory.

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

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

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

[5]  Duc Truong Pham,et al.  Adaptive control of dynamic systems using neural networks , 1993, Proceedings of IEEE Systems Man and Cybernetics Conference - SMC.

[6]  Kurt Hornik,et al.  Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks , 1990, Neural Networks.

[7]  P. Werbos,et al.  Beyond Regression : "New Tools for Prediction and Analysis in the Behavioral Sciences , 1974 .

[8]  James D. Keeler,et al.  Layered Neural Networks with Gaussian Hidden Units as Universal Approximations , 1990, Neural Computation.

[9]  K.S. Narendra,et al.  Intelligent control using neural networks , 1992, IEEE Control Systems.

[10]  Richard S. Sutton,et al.  Computational Schemes and Neural Network Models for Formation and Control of Multijoint Arm Trajectory , 1995 .

[11]  Kumpati S. Narendra,et al.  Control of nonlinear dynamical systems using neural networks: controllability and stabilization , 1993, IEEE Trans. Neural Networks.

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

[13]  Arjan van der Schaft,et al.  Non-linear dynamical control systems , 1990 .

[14]  A. Isidori.  Nonlinear Control Systems , 1985 .

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

[16]  P. Falb,et al.  Decoupling in the design and synthesis of multivariable control systems , 1967, IEEE Transactions on Automatic Control.