Adaptive Control For Switched Nonlinear Systems With Unmodeled Dynamic Uncertainties

Switched systems have been widely used to characterize the dynamic processes with switching properties.Unmodeled dynamic uncertainties always exist when we try to model the control plant,because of the existence of system complexities,model uncertainties and measurement errors.Such dynamic uncertainties will result in the poor performance of control schemes and instability of closed-loop systems.It should be mentioned that most of the existing approaches against unmodeled dynamics are for non-switched systems,while there are few results reported on switched systems.Motivated by the problems discussed above,this paper focuses on the adaptive control of switched nonlinear systems with unmodeled dynamic uncertainties,by using the backstepping control design technique and also by combining with the stability analysis approaches of Lyapunov function,average dwell-time and small-gain theorem.The contributions of this paper are summarized as follows:1.We investigate the adaptive control of switched nonlinear systems with unmodeled dynamic uncertainties and output hysteresis.It will be difficult to determine the system's input-to-output gain when the output channel suffers from hysteresis constraints.Namely,the small-gain theorem is difficult to be employed in the stability analysis of closed-loop systems.For this reason,we introduce a dynamic signal to dominate the unmodeled dynamic uncertainties,so as to avoid the determination of input-to-output gains.And then,we introduce the Nussbaum-gain technique in the control design procedure to solve the unknown high-frequency gain problem aroused by the output hysteresis successfully.2.We investigate the adaptive control of switched nonlinear systems with unstable unmodeled dynamic uncertainties.We firstly design an output feedback adaptive controller with the backsteppin technique.And then,we also present a timedependent switching law.In the proposed control scheme,we only need to update two adaptive parameters online,which means we can reduce the computing complexities significantly.Finally,by using the nonlinear small-gain theorem,we prove that the closed-loop system's output converges to a small region of zero,and meanwhile,all of the closed-loop signals are bounded.3.Based on the main result of the second contribution above,we further investigate the situation that the dynamic uncertainties do not contain stable modes.In such model,the dynamic disturbances are with nonstrict-feedback structures.It means we cannot employ the traditional backstepping technique directly.To solve this problem,we separate the state variables with the special property of radial basis function neural networks.Since the dynamic uncertainties do not contain stable modes,we need to constrain the switching law with fast and slow average dwell-time conditions.Finally,we prove the effectiveness of our proposed approach with the nonlinear small-gain theorem.