Adaptive Regulation in Switched Linear Systems

This paper considers an adaptive regulation problem for switched linear systems where it is desired to achieve regulation against unknown disturbance or reference signals. Switching among plant models as well as among disturbance and reference signals is defined according to a switching surface. The design of the proposed adaptive regulators involves three main steps. First, a set of observer-based Q-parameterized stabilizing controllers for the switched system is constructed. The stability properties for the resulting closed loop switched system are analyzed. Second, for each subsystem in the switched system, a set of Q-parameters needed to achieve regulation is derived by solving a set of interpolation conditions, and a sufficient regulation condition for the switched system is presented. Third, an adaptive algorithm is developed to tune the Q parameter in the expression of the parameterized controller to converge to the desired Q parameter that guarantees regulation for the switched system. Finally, a numerical example is presented to illustrate the effectiveness of the proposed method.