Neural-Network-Based Adaptive Control of Uncertain MIMO Singularly Perturbed Systems With Full-State Constraints

This article investigates the tracking control problem for a class of nonlinear multi-input-multi-output (MIMO) uncertain singularly perturbed systems (SPSs) with full-state constraints. The underlying issues become more challenging because two-time-scale characteristics and full state constraints are involved. To this end, first, the adaptive neural network (NN) control method is designed to handle system uncertainties in the design process. Second, the nonlinear state-dependent coordinate transformation functions are employed to avoid the violation of full-state constraints and feasibility conditions for intermediate controllers. Furthermore, by introducing an appropriate ε -dependent Lyapunov function, the potential ill-conditioned numerical problems in the design process of SPSs are avoided, and the stability of the nonlinear SPSs is proven. Finally, two examples are presented to illustrate the validity of the proposed adaptive NN control scheme.