具未知參數切換式系統之適應控制：分析與設計

Abstract

A switched system consists of several continuous dynamics and a switching signal that governs the activation of the corresponding dynamics among all subsystems. Control of fast varying systems has been a challenging task in control theory and switched systems can be regarded as such systems since they possess fast variations due to switching dynamics. Recently, stability analysis and control of switched systems have attracted much attentions. In this thesis, adaptive control of switched systems with unknown parameters and unknown switching signals is considered. The main challenge of control design for switched systems lies in the unamenability of the stability theories for analysis of such systems. We first analyze the stability properties of switched systems with traditional adaptive control schemes, and then we propose variable structure (VS) based adaptive control for the considered problem and integrate theories of adaptive control and switched systems to provide the solution in terms of the properties of switching signals. With the proposed VS adaptive control, stability and performance of the considered systems can be guaranteed under the conditions in terms of the switching signals. For the variable structure-model reference adaptive control (VS-MRAC) scheme, output tracking error is shown to be proportional to the designed gains, analogous to the non-switched system case. The switching signal condition is conservative due to parameters being unknown. For the VS adaptive backstepping control scheme, we can explicitly and accurately derive the conditions of switching signal. Moreover, thorough theoretic analysis on the proposed design is performed and simulation examples are provided to validate the analysis.