Abstract
We resolve the control problem for a class of dynamic hybrid systems (DHS) considering electrical systems as case study. The objective is to guarantee that the plan never reaches unsafe states. We consider a subclass class of DHS called Cumulative Preemptive Event-driven DHS (CPE-DHS). This class is distinguished by the dominance of its discrete aspect characterized by features as cumulative continuous variables combined with actions behavior that may be interrupted and restarted. We utilize a subclass of Rectangular Hybrid Automata (RHA), named Constant Slope RHA (CSRHA), as a solution framework to resolve the control problem. The main contribution is a control Algorithm for the class of systems described above. This algorithm ensures that the system meet the requirement specifications by forcing some events. The forcing action is given in the form of restrictions on the transition guards of the CSRHA. The termination/ decidability as well as correctness of the algorithm is given by theorems and formal proofs. This contribution ensures that the system will always be safe states and avoid failure due to the reachability of unsafe states. Our approach can be applied to a large category of industrial systems, especially electrical systems that we consider as case study.