Quotient-based Control Synthesis for Non-Deterministic Plants with Mu-Calculus Specifications

Samik Basu, Ratnesh Kumar
2006 Proceedings of the 45th IEEE Conference on Decision and Control  
We study the control of a nondeterministic discrete event system (DES) subject to a control specification expressed in the propositional mu-calculus, under complete observation of events. Given a plant automaton model and a mu-calculus specification we provide a set of rules that computes the "quotient" of the specification against the plant, which is another mu-calculus formula such that a supervisor exists if and only if the quotiented formula is satisfiable. Thus the control problem is
more » ... d to one of mu-calculus satisfiability. We also present a tableau-based satisfiability solving algorithm that identifies a model for the quotiented formula. The resulting model serves as a supervisor. The complexity of supervisor existence verification as well as model synthesis is single exponential in the size of the plant as well as the size of the specification formula.
doi:10.1109/cdc.2006.376737 dblp:conf/cdc/0001006a fatcat:q3b6r65kmfewtelbyjcmhkzp2y