Supervisory control for opacity of discrete event systems

In previous papers, we investigated the properties of opacity and we discussed the modification of the languages to satisfy the strong opacity, weak opacity, and no opacity in the framework of discrete event systems. In this paper, we study how to ensure strong opacity, weak opacity and no opacity by a supervisory control. If strong opacity, weak opacity or no opacity is not satisfied, then we can restrict the system´s behavior by a supervisor so that strong opacity, weak opacity or no opacity is satisfied. We consider the strong opacity control problem (SOCP), weak opacity control problem (WOCP) and no opacity control problem (NOCP). We characterize the solutions to SOCP in terms of the largest sublanguage that is controllable, observable (or normal), and strongly opaque. Similar characterization is available for solutions to NOCP. We also show that solutions to WOCP do not exist. We present formulas and algorithms for finding solutions to SOCP and NOCP. Examples are given to illustrate the results.