Control-law synthesis for linear hybrid systems

Based on the framework of hybrid automata the notion of controllability for a hybrid system with respect to given specifications is discussed. A hybrid system is defined as being controllable if there exists at least one acceptable run between each ordered pair of marked states, that is, the system can be controlled to satisfy all specifications while transferring between two marked states. Given certain restrictions, controllability can be decided for the class of linear hybrid systems and, if controllable, a set of control laws can be synthesized that guarantee a correct execution of the acceptable run. An algorithm for the generation of such control laws is presented. In general, the problem is only semidecidable since the algorithm does not necessarily terminate.<>