A Uniform Approach for Synthesizing Property-Enforcing Supervisors for Partially-Observed Discrete-Event Systems

Abstract

The problem under consideration in this paper is that of enforcement by supervisory control of a given property on a partially-observed discrete-event system. We present a general methodology that is applicable to a large class of properties previously studied (individually) in the literature. These properties include, but are not restricted to, safety, diagnosability, opacity, detectability, anonymity and attractability. When the given system does not satisfy the considered property, the objective is to synthesize a supervisor that restricts the system's behavior and provably enforces the given property; moreover, it is required that this supervisor be maximally permissive. We consider the general case where the system's events are partitioned into observable and unobservable events, and controllable and uncontrollable events, and we do not make any assumptions about these two partitions; in particular, we do not assume that all controllable events are observable. Our uniform approach first maps the considered property to a suitably-defined information state for the partially-observed system and then develops a supervisor synthesis methodology based on a finite bipartite transition system that embeds all reachable information states and all admissible supervisory control strategies. This transition system is called the All Enforcement Structure (or AES). We present an algorithm for the construction of the AES and discuss its properties. Then we use the AES to develop a synthesis algorithm that constructs a supervisor that is provably property enforcing and maximally permissive. We illustrate the application of our uniform approach to the enforcement of the above-mentioned properties.

Supervisor localization of discrete-event systems under partial observation

“…i = ζ α (i 0 , P (s))), there holds ζ α (i, α)!. By the definition of ζ α in (15), there exists an uncertainty set Fig. 3.…”

K-delayed strong detectability of discrete-event systems

“…We next give polynomial-time synthesis algorithms for enforcing delayed strong detectability of FSAs by using the verification methods given in Section 3 and Section 4. The synthesis problem considered in our paper is not totally the same as the one in the supervisory control framework [11,14,18,20]. For the supervisory control framework, the synthesis problem is to disable controllable events according to observed labeling sequences, but does not directly depend on structure of a DES.…”

“…Note that in the supervisory control framework, to the best of our knowledge, all known existing algorithms for enforcing delayed strong detectability run in exponential time, see, for example, ω-strong detectability is considered in [14], * -(k 1 , k 2 )-detectability is considered in [20], because the usage of a notion of observer (a deterministic finite automaton that is of exponential size of the considered DES) is indispensable. The synthesis algorithm for enforcing a stronger version of * -strong detectability (obtained by letting the number K in Definition 2 equal to 0, pulling out "∃k ∈ N" in Definition 2 and putting "with respect to a given k ∈ N" before "if") under the liveness assumption (a little weaker than ii) of Assumption 1) given in [18] is also of exponential-time complexity. The synthesis problem for enforcing ω-strong detectability is also studied in [11] by online sensor activation, where the overall computational complexity is also exponential of the size of the considered DES, based on construction of an automaton square of the size of an observer.…”

Estimation and Verification of Partially Observed Discrete‐Event Systems

“…In [88], the authors studied the problem of synthesizing supervisors that enforce detectability. A uniform approach for control synthesis for enforcing a wide class of properties was recently proposed by Yin and Lafortune in a series of papers [119,120,123,126].…”