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Adaptive Control/Identification for Hybrid Systems Part I: with Bounded 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 address these problems for systems with bounded discrete regressor. This assumption may appear restrictive at first sight, but its interest lies in that it yields a fairly simple static discrete adaptation law. Furthermore, parameter-estimation convergence is guaranteed under an original property of persistency of excitation tailored for hybrid systems, which is introduced here. The main results rely on Lyapunov theory for hybrid systems and establish uniform global asymptotic stability for the resulting closed-loop hybrid system. In the companion paper [1] the boundedness assumption on the regressor is relaxed and a high-order discrete adaptation law is proposed.