Indirect Adaptive Control of Piecewise Affine Systems without Common Lyapunov Functions

In this letter, we propose a novel indirect model reference adaptive control approach for uncertain piecewise affine systems. This approach exploits a barrier Lyapunov function to construct novel adaptation laws and average dwell time constraints for switching. Compared to the previous research, where closed-loop stability and asymptotic tracking can only be established with a common Lyapunov function, the current approach allows a multiple Lyapunov function setting and enables broader applications. Furthermore, the estimation errors of control gains and subsystem parameters are proved to converge to zero asymptotically if a persistent excitation condition is satisfied. A simulation example of the pitch control of a helicopter system shows the effectiveness of the proposed approach.