Model reference adaptive control of piecewise affine systems with state tracking performance guarantees

• Published in: International journal of robust and nonlinear control 2022-05, Vol.32 (7), p.4129-4148
• Main Authors: Liu, Tong, Buss, Martin
• Format: Article
• Language: English
• Subjects: Adaptive control; barrier Lyapunov function; Dwell time; Liapunov functions; Model reference adaptive control; piecewise affine systems; robust adaptive control; Robustness (mathematics); Switching; time‐varying performance guarantees; Tracking errors
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.6015

In this paper, we investigate the model reference adaptive control approach for uncertain piecewise affine systems with state tracking performance guarantees. The proposed approach ensures the error metric, defined as the weighted Euclidean norm of the state tracking error, to be confined within a user‐defined time‐varying performance bound. We introduce an auxiliary performance bound to construct a barrier Lyapunov function. This auxiliary performance bound is reset at each switching instant, which prevents the barrier transgression caused by the jumps of the error metric at switching instants. The dwell time constraints are derived such that the auxiliary performance bound resides within the user‐defined performance bound. We prove that the Lyapunov function is nonincreasing at and in between the switching instants. Therefore, it does not impose extra dwell time constraints and ensures the error metric to fulfill the performance guarantees. Furthermore, we study the robust modification of the adaptive controller for the uncertain piecewise affine systems subject to unmatched disturbances. A numerical example validates the correctness of the proposed approach.