Model reference adaptive control for nonlinear time‐varying hybrid dynamical systems

• Published in: International journal of adaptive control and signal processing 2023-08, Vol.37 (8), p.2162-2183
• Main Author: L'Afflitto, Andrea
• Format: Article
• Language: English
• Subjects: Adaptive systems; Control theory; Dynamical systems; hybrid dynamical systems; Hybrid systems; LaSalle–Yoshizawa theorem; Mathematical analysis; Mathematical models; Model reference adaptive control; Nonlinear control; Tracking errors; Trajectory control
• ISSN: 0890-6327; 1099-1115
• DOI: 10.1002/acs.3631

Summary This paper presents the first model reference adaptive control system for nonlinear, time‐varying, hybrid dynamical plants affected by matched and parametric uncertainties, whose resetting events are unknown functions of time and the plant's state. In addition to a control law and an adaptive law, which resemble those of the classical model reference adaptive control framework for continuous‐time dynamical systems, the proposed framework allows imposing instantaneous variations in the reference model's trajectory to rapidly steer the trajectory tracking error to zero, while retaining the closed‐loop system's ability to follow a user‐defined signal. These results are enabled by the first extension of the classical LaSalle–Yoshizawa theorem to time‐varying hybrid dynamical systems, which is presented in this paper as well. A numerical simulation shows the key features of the proposed adaptive control system and highlights its ability to reduce both the control effort and the trajectory tracking error over a classical model reference adaptive control system applied to the same problem.