Neural Network L (1) Adaptive Control of MIMO Systems with Nonlinear Uncertainty

An indirect adaptive controller is developed for a class of multiple-input multiple-output (MIMO) nonlinear systems with unknown uncertainties. This control system is comprised of an L (1) adaptive controller and an auxiliary neural network (NN) compensation controller. The L (1) adaptive controller has guaranteed transient response in addition to stable tracking. In this architecture, a low-pass filter is adopted to guarantee fast adaptive rate without generating high-frequency oscillations in control signals. The auxiliary compensation controller is designed to approximate the unknown nonlinear functions by MIMO RBF neural networks to suppress the influence of uncertainties. NN weights are tuned on-line with no prior training and the project operator ensures the weights bounded. The global stability of the closed-system is derived based on the Lyapunov function. Numerical simulations of an MIMO system coupled with nonlinear uncertainties are used to illustrate the practical potential of our theoretical results.