Small-Gain Technique-Based Adaptive NN Control for Switched Pure-Feedback Nonlinear Systems

This paper focuses on the problem of adaptive neural networks (NNs) tracking control for a class of completely nonaffine switched pure-feedback uncertain nonlinear systems with switched reference model. A sufficient and necessary condition for the control problem to be solvable is derived by exploiting the common Lyapunov function (CLF) method, backstepping, input-to-state stability analysis, and the small-gain technique. Also, a small-gain technique-based adaptive NN control scheme is provided to avoid the designed difficulty caused by the construction of an overall CLF for the switched closed-loop system, which is usually required when studying the switched pure-feedback system. Adaptive NN controllers of individual subsystems are constructed to guarantee that all of the signals in the closed-loop system are semi-globally uniformly ultimately bounded under arbitrary switchings, and the tracking error converges to a small neighborhood of the origin. Two examples, which include a continuously stirred tank reactor system, are presented to demonstrate the effectiveness of the proposed design approach.