Data-driven hybrid switched-gain estimation for hybrid systems with periodic jumps

Accurate state estimation is fundamental for the control and analysis of hybrid systems. Significant progress has been made using model-based observers. However, their performance depends on an accurate system model, which is often difficult to obtain such a model. This is especially true for unknown hybrid systems with periodic jumps. To address this gap, this paper presents two classes of data-driven estimation approaches for unknown hybrid systems with periodic jumps. An estimation law is constructed directly from noisy input/measured data using the S-lemma. Systems explaining the data are derived for unknown dynamical hybrid systems by virtue of the behavioral theory of systems. A criterion on global exponential stability is established by employing data-based linear matrix inequalities. A data-driven hybrid estimation scheme is designed to eliminate the system model identification step. Under mild conditions, the global exponential stability of systems explaining the data is guaranteed theoretically. In particular, the obtained results are applied to a data-driven hybrid switched-gain estimation framework. The effectiveness of the proposed approaches is demonstrated through simulations applied to fully actuated walking robots.