Adaptive Control/Identification for Hybrid Systems, Part II: with Linear-growth-order Discrete Regressor

In this and the companion paper [1] we propose a direct-adaptive-control framework for hybrid dynamical systems with unknown parameters. The approach addresses both the tracking-control and the parameter-estimation problems and relies on Lyapunov theory for hybrid systems. In this paper, we extend the main results of [1] to deal with hybrid systems that contain a regressor that is of linear order of growth, thereby relaxing the boundedness restriction imposed in [1]. As in the latter reference, the statements rely on Lyapunov theory for hybrid systems and we establish uniform global asymptotic stability in closed loop. In particular, parameter-estimation convergence is guaranteed when a generic hybrid persistence of excitation condition on the pair of discrete and continuous regressor functions holds. On the other hand, the relaxation of the boundedness assumption relies on a higher-order adaptation law.