Safety controller design for incrementally stable switched systems using event-based symbolic models

In this paper, we investigate the problem of lazy safety controllers synthesis for event-based symbolic models of incrementally stable switched systems with aperiodic time sampling. First of all, we provide a novel event-based scheme for symbolic models design. The obtained symbolic models are computed while considering all transitions of different durations satisfying a triggering condition. In addition, they are related to the original switched system by a feedback refinement relation and thus useful for control applications. Then, using the particular structure of the obtained event-based symbolic model, a lazy safety controller is designed while choosing transitions of longest durations. Secondly, for the same state sampling parameter and desired precision, we show that the obtained event-based symbolic model is related by a feedback refinement relation to the classical symbolic model designed for incrementally stable switched systems with periodic time sampling. Based on this relationship, we prove analytically that the size of the set of controllable states obtained with the lazy safety controller designed for an event-based symbolic model is larger than the one obtained with a safety controller designed for the classical symbolic model. Finally, an illustrative example is proposed in order to show the efficiency of the proposed method and simulations are performed for a Boost DC-DC converter structure.