Supervisory control of discrete event systems for bisimulation or simulation equivalence

The supervisory control of discrete event systems provides a framework for control of eventdriven systems. Applications of supervisory control theory include protocol design for communication processes, control logic synthesis in manufacturing systems, and collision avoidance in human-computer interaction systems. When designing a system at a certain level of abstraction, lower level details of the system and its specification are normally omitted to obtain higher level models that may be (nondeterministic) event-driven systems. Nondeterministic systems exhibit both branching and sequential behaviors and are captured using bisimulation equivalence (the traditional language equivalence only captures sequential behaviors). Simulation equivalence is more expressive than language equivalence but captures only the universal fragment of branching behaviors. This dissertation presents supervisory control of discrete event systems for enforcing bisimulation equivalence or simulation equivalence with respect to given specifications. We show that in the general setting of nondeterministic systems and specifications, the complexity for bisimilarity enforcing control is doubly exponential and for similarity enforcing control remains polynomial solvable. So the choice of behavioral equivalence used depends on the application at hand and there is a trade-off between the expressivity and the complexity. We further show that the bisimilarity enforcing control problem becomes polynomially solvable when the system model is deterministic and there is complete observability of events. When the complete observability requirement is relaxed, the control existence problem remains polynomially solvable and the control synthesis problem becomes singly exponential. These complexities are similar to the ones for control under partial observation in completely deterministic setting Tsitsiklis (1989).