Discrete-time neural network control of nonlinear systems in non-strict feedback form

In this paper, an adaptive multilayer neural-network (NN) controller is designed to deliver a desired tracking performance for the control of a class of unknown nonlinear systems in discrete time where the system is expressed in non-strict feedback form. Three NNs are used where two NNs approximate the dynamics of the nonlinear system whereas the third critic NN generates a critic signal, which is used to tune the weights of the action generating NNs. The NN control scheme uses backstepping approach and presents a well-defined controller design. The stability analysis of the closed-loop control system is given and the uniform ultimately boundedness (UUB) of the closed-loop tracking error is shown.

[1]  I. Kanellakopoulos,et al.  Systematic Design of Adaptive Controllers for Feedback Linearizable Systems , 1991, 1991 American Control Conference.

[2]  S. Ge,et al.  Adaptive NN control for a class of strict-feedback discrete-time nonlinear systems via backstepping , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[3]  Sarangapani Jagannathan,et al.  Control of a class of nonlinear discrete-time systems using multilayer neural networks , 2001, IEEE Trans. Neural Networks.

[4]  Frank L. Lewis,et al.  Backlash compensation with filtered prediction in discrete time nonlinear systems by dynamic inversion using neural networks , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

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

[6]  P.V. Kokotovic,et al.  The joy of feedback: nonlinear and adaptive , 1992, IEEE Control Systems.