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

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.