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

Abstract

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.

Robust model reference tracking control for high‐order descriptor linear systems subject to parameter uncertainties

“…then the output of the closed-loop HODLS (9) and the desired output generated from the reference model ( 4) satisfy the zero-error asymptotic tracking property:…”

“…□ Remark 3. When conditions in Lemma 3 hold, the closedloop HODLS (9) and the corresponding uncertain closed-loop system (33) have stability (regularity, impulse-free, and asymptotically stability) in common. Thus, the RPPDSFS problem can be solved via robust eigenstructure assignment approaches in [25,31] or other methods in [29].…”

“…Model reference tracking control problem, also named model following control problem, arises from physical applications [1], such as robotic systems [2,3], aircraft [4], helicopter systems [5,6] and its purpose is to make the closed-loop system match a given reference system (in other words, the states track the reference system states) and/or the outputs of the closedloop system follow the reference model outputs. Due to the existence of unknown parameters and/or parameters changing with time in the model, the adaptive technique is used to handle the model reference tracking control problem [7][8][9][10][11]. The other eye-catching technique is to construct a controller with a feed-forward compensator, and excellent work has been completed.…”