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This paper investigates the problem of co-synthesis of edit function andsupervisor for opacity enforcement in the supervisory control of discrete-eventsystems (DES), assuming the presence of an external (passive) intruder, wherethe following goals need to be achieved: 1) the external intruder should neverinfer the system secret, i.e., the system is opaque, and never be sure aboutthe existence of the edit function, i.e., the edit function remains covert; 2)the controlled plant behaviors should satisfy some safety and nonblockingnessrequirements, in the presence of the edit function. We focus on the class ofedit functions that satisfy the following properties: 1) the observationcapability of the edit function in general can be different from those of thesupervisor and the intruder; 2) the edit function can implement insertion,deletion, and replacement operations; 3) the edit function performs boundededit operations, i.e., the length of each string output of the edit function isupper bounded by a given constant. We propose an approach to solve thisco-synthesis problem by modeling it as a distributed supervisor synthesisproblem in the Ramadge-Wonham supervisory control framework. By taking thespecial structure of this distributed supervisor synthesis problem intoconsideration and to improve the possibility of finding a non-empty distributedsupervisor, we propose two novel synthesis heuristics that incrementallysynthesize the supervisor and the edit function. The effectiveness of ourapproach is illustrated on an example in the enforcement of the locationprivacy.

Privacy-Preserving Supervisory Control of Discrete-Event Systems via  Co-Synthesis of Edit Function and Supervisor for Opacity Enforcement and  Requirement Satisfaction