Variable structure based switching adaptive control for a class of unknown switched linear systems

In this paper, we discuss the model reference adaptive control problem of switched linear systems with unknown parameters. Since we do not have information about the system parameters nor the possible abrupt changes of parameters, conventional integral adaptive law do not function well for switched systems. We propose a variable structure based adaptive controller to the switched system and show error convergence and signal boundedness for a class of switching signals by multiple Lyapunov function theory. A sufficient condition for stability and error convergence of the switched system with unknown parameters is given. To improve the chattering phenomenon, we propose a switching adaptive controller that switches between the leakage type and the VS adaptive controller by hysteresis switching algorithm. Simulation results are provided to support the analysis.