State transformation-based adaptive tracking control for a class of nonlinear systems with time-varying state constraints.

It is meaningful to study the control problems of nonlinear systems with uncertain parameters and external disturbances, especially for those subject to state constraints. In this paper, a state transformation approach is proposed to address time-varying asymmetric state constraints. By this state transformation, the state constrained problem is transformed into the boundedness problem of the transformed function. When the initial states are in the constrained region, the state constraints can be guaranteed as long as the boundedness of the transformed functions are guaranteed. Compared with the barrier Lyapunov function (BLF) approach, it successfully removes the feasibility test from virtual controllers, and thus broadens its application scope. In addition, for the parametric uncertainties and external disturbances exist in the system simultaneously, the tuning function and the adaptive laws for the upper bounds of disturbances are designed to help realize the control performance of the system. Consequently, a novel tuning function based adaptive backstepping control scheme is given. The designed controller ensures the error signals converge to a small neighbourhood of zero and the asymmetric time-varying constraints on system states are maintained for all the time. Finally, simulation results are given to illustrate the efficacy of the presented control scheme.