Robust adaptive tracking control of uncertain slowly switched linear systems

In this paper, robust adaptive tracking control schemes for uncertain switched linear systems subject to disturbances are investigated. The robust adaptive control problem requires the design of both adaptive and switching laws. A novel adaptive law is proposed based on an extended leakage approach, which does not require knowledge of the bounds of the uncertainty set. Two switching laws are developed based on extended dwell time (DT) strategies: (a) mode-dependent dwell time (MDDT); (b) mode-mode-dependent dwell time (MMDDT). MDDT exploits the information of the known reference model for every subsystem, i.e., the dwell time is realized in a subsystem sense. MMDDT is a variant of MDDT that can guarantee stability under faster switching than MDDT, provided that the next subsystem to be switched on is known. The proposed adaptive schemes can achieve global uniform ultimate boundedness for shorter switching intervals than state-of-the-art adaptive approaches based on DT. In addition to global uniform ultimate bounded stability, transient and steady-state performance bounds are derived for the tracking error. The numerical example of a highly maneuverable aircraft technology vehicle is adopted to demonstrate the effectiveness of the proposed adaptive methods.