Safety-Critical Model Reference Adaptive Control of Switched Nonlinear Systems With Unsafe Subsystems: A State-Dependent Switching Approach.

Abstract

In this article, a novel safety-critical model reference adaptive control approach is established to solve the safety control problem of switched uncertain nonlinear systems, where the safety of subsystems is unnecessary. The considered switched reference model consists of submodels possessing safe system behaviors that are governed by switching signals to achieve satisfactory performances. A state-dependent switching control technique based on the time-varying safe sets is proposed by utilizing the multiple Lyapunov functions method, which guarantees the state of the subsystem is within the corresponding safe set when the subsystem is activated. To deal with uncertainties, a switched adaptive controller with different update laws is constructed by resorting to the projection operator, which reduces the conservatism caused by the common update law adopted in all subsystems. Moreover, a sufficient condition is obtained by structuring a switched time-varying safety function, which ensures the safety of switched systems and the boundedness of error systems in the presence of uncertainties. As a special case, the safety control problem under arbitrary switching is considered and a corollary is deduced. Finally, a numerical example and a wing rock dynamics model are provided to verify the effectiveness of the developed approach.