Synthesis and viability of minimally interventive legal controllers for hybrid systems

In this paper, we study the control of Composite Hybrid Machines (CHMs) subject to safety specifications. CHMs are a fairly general class of hybrid systems modeled in modular fashion as the concurrent operation of Elementary Hybrid Machines (EHMs). The formalism has a well-defined synchronous-composition operation that permits the introduction of the controller as a component of the system. The task of a legal (safety) controller is to ensure that the system never exits a set of specified legal configurations. Among the legal controllers, we are particularly interested in designing a minimally-interventive (or minimally-restrictive) one, which interferes in the system's operation only when constraint violation is otherwise inevitable. Thus, a minimally interventive safety controller provides maximum flexibility in embedding additional controllers designed for other control objectives to operate concurrently while eliminating the need to re-investigate or re-verify the legality of the composite controller with respect to the safety specification. We describe in detail an algorithm for controller synthesis and examine the viability of a synthesized controller as related to the possibility of Zenoness, where the system can undergo an unbounded number of transitions in a bounded length of time.