Adaptive exact tracking control for a class of uncertain nonlinear switched systems with arbitrary switchings

This paper investigates the exact tracking control problem for a class of uncertain nonlinear switched systems with arbitrary switchings. Two mode-dependent adaptive backstepping state feedback control schemes are presented, where unknown switching parameters are directly estimated via switched adaptive laws. To avoid the loss of adaptive information due to persistent switching of the plant, the adaptive parameters are reset at the switching instants by exploiting the previous estimation information, which is called the trajectory initialization method. By constructing a novel common Lyapunov function, it is proven that the designed controller ensures the exact tracking of the closed-loop system. To improve the transient performance, especially at switching instants, the prescribed performance technique is incorporated into the first scheme without destroying the asymptotic behavior. It is shown that all the state tracking errors remain within the predefined performance bounds. Finally, simulation results on a mass-spring-damper system are provided to demonstrate the effectiveness of the proposed approaches.