Symbolic On-the-Fly Synthesis in Supervisory Control Theory

This paper presents an efficient synthesis algorithm and its proof of correctness for computing the controllable, nonblocking, and minimally restrictive supervisor in the supervisory control theory. Conventional synthesis algorithms are based on backward reachability computations, where blocking and uncontrollable states are iteratively found by searching the entire state space several times until a fixed point is reached. Many unnecessary states may be visited in this kind of searching. In this paper, we present an alternative synthesis algorithm based on forward reachability, where a number of synthesis steps are performed during the reachability computations. This approach is inspired from the search techniques in Artificial Intelligence (AI) planning. To handle large-scale problems, the algorithm performs the computations symbolically based on binary decision diagrams. The algorithm has been developed, implemented, and applied to several large-scale benchmarks. It is shown that, on average, the on-the-fly algorithm is more efficient than the conventional synthesis algorithms, in particular for problems with many uncontrollable states.