Showing papers by "Tomáš Masopust published in 2015"

Coordination control of discrete-event systems revisited

Abstract: In this paper, we revise and further investigate the coordination control approach proposed for supervisory control of distributed discrete-event systems with synchronous communication based on the Ramadge-Wonham automata framework. The notions of conditional decomposability, conditional controllability, and conditional closedness ensuring the existence of a solution are carefully revised and simplified. The approach is generalized to non-prefix-closed languages, that is, supremal conditionally controllable sublanguages of not necessary prefix-closed languages are discussed. Non-prefix-closed languages introduce the blocking issue into coordination control, hence a procedure to compute a coordinator for nonblockingness is included. The optimization problem concerning the size of a coordinator is under investigation. We prove that to find the minimal extension of the coordinator event set for which a given specification language is conditionally decomposable is NP-hard. In other words, unless P=NP, it is not possible to find a polynomial algorithm to compute the minimal coordinator with respect to the number of events.

Supervisory Control of Discrete-Event Systems

Abstract: The aim of this essay is to provide a brief introduction to supervisory control theory of discrete-event systems

On a distributed computation of supervisors in modular supervisory control

Abstract: We discuss a supervisory control problem of modular discrete-event systems that admits a distributed computation of supervisors. We provide a characterization and an algorithm to compute the supervisors. If the specification cannot be reached, we make use of a relaxation of coordination control to compute a sublanguage of the specification for which the supervisors can be computed in a distributed way.

On the Complexity of k-Piecewise Testability and the Depth of Automata

Abstract: For a non-negative integer k, a language is k-piecewise testable (k-PT) if it is a finite boolean combination of languages of the form \(\varSigma ^* a_1 \varSigma ^* \cdots \varSigma ^* a_n \varSigma ^*\) for \(a_i\in \varSigma \) and \(0\le n \le k\). We study the following problem: Given a DFA recognizing a piecewise testable language, decide whether the language is k-PT. We provide a complexity bound and a detailed analysis for small k’s. The result can be used to find the minimal k for which the language is k-PT. We show that the upper bound on k given by the depth of the minimal DFA can be exponentially bigger than the minimal possible k, and provide a tight upper bound on the depth of the minimal DFA recognizing a k-PT language.

Computation of Controllable and Coobservable Sublanguages in Decentralized Supervisory Control via Communication

Abstract: In decentralized supervisory control, several local supervisors cooperate to accomplish a common goal (specification). Controllability and coobservability are the key conditions to achieve a specification in the controlled system. We construct a controllable and coobservable sublanguage of the specification by using additional communications between supervisors. Namely, we extend observable events of local supervisors via communication and apply a fully decentralized computation of local supervisors. Coobservability is then guaranteed by construction. Sufficient conditions to achieve the centralized optimal solution are discussed. Our approach can be used for both prefix-closed and non-prefix-closed specifications.

Relative observability in coordination control

Abstract: Relative observability was introduced and studied in the framework of partially observed discrete-event systems as a condition stronger than observability and weaker than normality. Unlike observability, relative observability is closed under language unions, which makes it interesting for practical applications. In this paper, we investigate this notion in the framework of coordination control. We prove that conditional normality is stronger than conditional relative observability, hence it can be used in coordination control instead of conditional normality. We present a distributive procedure to compute a conditionally controllable and conditionally observable sublanguage of the specification that contains the supremal conditionally relative observable sublanguage.

Combined Top-down and Bottom-up Approach to Multilevel Supervisory Control

Abstract: Recently, we have proposed two complementary approaches, top-down and bottom-up, to multilevel supervisory control of discrete-event systems. In this paper, we compare and combine these approaches. The combined approach has strong features of both approaches, namely, a lower complexity of the top-down approach with the generality of the bottom-up approach. We show that, for prefix-closed languages, a posteriori supervisors computed in the bottom-up manner do not alter maximal permissiveness within the three-level coordination control architecture, that is, the supremal three-level conditionally-controllable and conditionally-normal language can always be computed in a distributed way using multilevel coordination. Moreover, a general polynomial-time procedure for non-prefix closed case is proposed based on coordinators for nonblockingness and a posteriori supervisors.

On the Computation of Controllable and Coobservable Sublanguages in Decentralized Supervisory Control.

Abstract: In decentralized supervisory control, several local control agents (supervisors) cooperate to achieve a common goal expressed by a safety specification and/or nonblockingness. Coobservability is the key condition to achieve the specification as the resulting language of the controlled system. One of the most important problems is thus to compute a coobservable sublanguage of the specification. In this paper, we show how to compute a controllable and coobservable sublanguage of the specification in a computationally efficient way. The method is motivated by recent results in coordination control of modular discrete-event systems, namely by the notion of conditional decomposability.

A Relaxed Framework for Coordination Control of Discrete-Event Systems

Abstract: In this paper, we simplify the coordination control approach by removing the supervisor for the coordinator from the closed-loop system and relax the restrictions placed on a coordinator. This relaxation results in the simplification of the whole coordination control framework, including the notions of conditional controllability, conditional observability, and conditional normality. Compared to our previous work, the role of the supervisor on a coordinator alphabet is postponed until the final stage of the coordination control synthesis. This completes and clarifies our previous results, while all the fundamental theorems remain valid in the relaxed framework. Unlike previous approaches we can always compute a conditionally controllable sublanguage without any restricting conditions we have used before.

Multilevel coordination control of partially observed modular DES

Abstract: Coordination control for multi-level discrete-event systems is generalized to supervisory control with partial observations. The multi-level system architecture is in this paper restricted to three levels, which include two levels of coordination on the two highest levels. At Level 1 a coordinator coordinates several coordinators of Level 2 and at Level 2 each coordinator coordinates a set of subsystems of Level 3. The problem is to synthesize a set of supervisors based on partial observations and on top-down synthesis, which together achieve the control objectives. A necessary and sufficient condition for the existence of such supervisors is three-level conditional controllability and three-level conditional observability. A procedure is formulated and proven (Theorem 16) to construct the supremal three-level conditionally controllable and conditionally normal sublanguage of the specification language.