Model reference robust adaptive control for a class of uncertain switched linear systems

Abstract

SUMMARYIn this paper, we proposed a model reference robust adaptive control approach for a class of uncertain switched linear systems, in which subsystems of the switched linear system are in control canonical form. The control architecture is composed of a switched reference system (SRS) and a switched adaptive controller (SAC). The SRS specifies the desired dynamics of the uncertain switched linear system, while the SAC makes the uncertain switched linear system dynamics track the SRS dynamics. By multiple Lyapunov functions method, we prove that the closed‐loop switched system is uniformly bounded under arbitrary switching laws, provided that a linear matrix inequality (LMI)‐based sufficient condition is satisfied. We apply the proposed approach to a typical servo‐hydraulic positioning system. The simulation results show that the proposed approach is fairly insensitive to disturbances, uncertainties and non‐smoothly varying dynamics, and performs better than a proportional‐derivative controller or a minimal controller synthesis controller. Copyright © 2011 John Wiley & Sons, Ltd.