Stable neural control of uncertain multivariable systems

Tracking control of a class of non-linear, uncertain, multi-input, multiple-output systems is addressed in this paper. The control system architecture uses neural networks for function approximation, certainty equivalent control inputs to cancel plant dynamics and smoothed sliding mode control to insure that the trajectories remain bounded. Lyapunov analysis is used to derive equations for the sliding mode control, neural network training, and to show uniform ultimate boundedness of the closed-loop system. Stability analysis results are shown for single-input single-output and two-input two-output systems. Results are then extended to the more general multiple-input multiple-output case where the number of inputs is equal to the number of outputs. Simple simulation examples are used to illustrate control system performance. Copyright (C) 2003 John Wiley Sons, Ltd.