Global tracking control of strict-feedback systems using neural networks.

Most existing adaptive neural controllers ensure semiglobally uniform ultimately bounded stability on the condition that the neural approximation remains valid for all time. However, such a condition is difficult to verify beforehand. As a result, deterioration of tracking performance or even instability may occur in real applications. A common recourse is to activate an extra robust controller outside the neural active region to pull back the transient. Such an approach, however, has been restricted to dynamic systems with matched uncertainty. We extend it to strict-feedback systems with mismatched uncertainties via multiswitching-based backstepping methodology. Each virtual and actual controller of the proposed design switches between an adaptive neural controller and a robust controller, with the switching algorithm being sufficiently smooth and, hence, able to be incorporated with the backstepping tool. The overall controller ensures globally uniform ultimate boundedness while simultaneously avoiding the possible control singularity. Simulation results demonstrate the validity of the proposed designs.