Adaptive control for hybrid dynamical systems with user-defined rate of convergence

Abstract

This paper presents a model reference adaptive control (MRAC) system for nonlinear, time-varying, hybrid dynamical plants affected by modeling uncertainties. This system is unique because, in addition to regulating the trajectory tracking error to zero, it allows the user to set the rate of convergence of the tracking error between consecutive resetting events. This proposed result has been possible by leveraging an auxiliary trajectory tracking error dynamics to accelerate convergence of the trajectory tracking error according to the two-layer MRAC framework. The resetting logic of both the reference model and the auxiliary trajectory tracking error dynamics bound variations in the trajectory tracking error due to undesired resetting events in the plant dynamics. The resetting events of the reference and auxiliary model also reduce the trajectory tracking error whenever some dwell-time condition is met. Finally, the resetting logic of both the reference model and the auxiliary trajectory tracking error reduces the control effort at isolated time-instants. Three numerical examples demonstrate the applicability of the proposed result as well as their advantages over alternative adaptive control techniques for nonlinear, time-varying, hybrid dynamical plants as well as classical MRAC.