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 capital sigma 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) capital sigma sub(l) for capital sigma , 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 capital sigma sub(l). We show that it also solves the control problem for the underlying hybrid system capital sigma . If no solution exists, approximation accuracy can be increased by computing the strongest k-complete abstraction capital sigma sub(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.