Adaptive predefined-time asymptotic tracking control for uncertain switched nonlinear systems with deferred constraints

This paper investigates the predefined-time asymptotic tracking control problem for uncertain switched nonlinear systems with deferred constraints, even when the predefined-time tracking control problem for each individual subsystem is not solvable. First, predefined-time stability criterion is obtained for switched nonlinear systems. Second, the states constraints can be transformed into the measurable states constraints by the conversion of constraints targets. Meanwhile, a new deferred constraint about the measurable states constraints has been proposed, which remove the restricted situation that the initial values of the measurement state must be within the constraint regions, and a novel nonlinear systems transformation including states and error unified function ensures tracking error and system states within a given function constraints ranges. Moreover, based on the predefined-time stability criterion, a predefined-time controller and an adaptive state dependent switching law are designed to ensure that all signal of the closed-loop system remain bounded. The tracking error can enter into the interval near origin in predefined time, and asymptotically tend towards to zero finally. To overcome the Zeno behavior, the modified switching dependent law is designed so that the numbers of switching times are decreased. The method is validated through a mass-spring-damper system.