Controller synthesis for hybrid systems with lower bounds on event separation

A systematic procedure for synthesizing all full-state feedback controllers for a hybrid system subject to a safety (state-invariance) specification has been proposed by Tomlin et al. (1998) and Lygeros et al. (1999). The interaction between the controller and a nondeterministic hybrid plant is viewed as a two-person game. The controller wins if it keeps the state of the closed-loop system within a specified set of good states; its adversarial environment tries to force the system outside the good set. The synthesis procedure iteratively augments the set of states from which the environment wins via either one additional discrete step, or one additional continuous flow. The key difficulty in carrying out the synthesis procedure lies in the computations for continuous flows. One must essentially solve a series of differential games in which the environment is trying to drive the system into its target set at the same time as avoiding the target set of the controller. We study hybrid systems with lower bounds on the separation between occurrence times of consecutive discrete moves. These systems arise when modeling minimal delay times between events, either in the controller, or in the environment. For such systems, we provide techniques for solving the differential games in reduced state spaces. The main idea is to discretize information about whether discrete moves are enabled or not