Discrete supervisory control of hybrid systems based on l-complete approximations

The topic of this paper is the synthesis of discrete supervisory control for hybrid systems Σ with discrete external signals. Such systems are in general neither l-complete nor can they be represented by finite state machines. Our solution to the control problem is as follows: we find the strongest l-complete approximation (abstraction) Σ_l for Σ, represent it by a finite state machine, and investigate the control problem for the approximation. If a solution exists on the approximation level, we synthesize the maximally permissive supervisor for Σ_l. We show that it also solves the control problem for the underlying hybrid system Σ. If no solution exists, approximation accuracy can be increased by computing the strongest k-complete abstraction Σ_k, k > l. The basic ideas regarding the approximation step are explained within the framework of Willems' behavioral systems theory. Implementation issues are treated in a state space framework, and the main results are interpreted from a traditional control engineering point of view.