Tomáš Masopust

Supervisory control synthesis of discrete-event systems using a coordination scheme

Supervisory control of distributed DES with a global specification and local supervisors is a difficult problem. For global specifications, the equivalent conditions for local control synthesis to equal global control synthesis may not be met. This paper formulates and solves a control synthesis problem for a generator with a global specification and with a combination of a coordinator and local controllers. Conditional controllability is proven to be an equivalent condition for the existence of such a coordinated controller. A procedure to compute the least restrictive solution within our coordination control architecture is provided and conditions under which the result coincides with the supremal controllable sublanguage are stated.

Control of Distributed Systems - Tutorial and Overview

Distributed systems consist of an interconnection of two or more subsystems. Control of such systems is structured by two or more controllers, each receiving an observation stream from a local subsystem and providing an input to the local subsystem. Coordinated distributed systems are defined for linear systems, for Gaussian systems, and for discrete-eventsystemsandanalgebraic-geometriccharacterization is provided. Coordination control of distributed systems requires a specific control synthesis procedure which is presented. Distributed control with communication between controllers is formulated and discussed.

On conditional decomposability

Abstract The requirement of a language to be conditionally decomposable is imposed on a specification language in the coordination supervisory control framework of discrete-event systems. In this paper, we present a polynomial-time algorithm for verification whether a language is conditionally decomposable with respect to given alphabets. Moreover, we also present a polynomial-time algorithm to extend the common alphabet so that the language becomes conditionally decomposable. A relationship of conditional decomposability to nonblockingness of modular discrete-event systems in general settings is also discussed in this paper. It is shown that conditional decomposability is a weaker condition than nonblockingness.

Efficient separability of regular languages by subsequences and suffixes

When can two regular word languages K and L be separated by a simple language? We investigate this question and consider separation by piecewise- and suffix-testable languages and variants thereof. We give characterizations of when two languages can be separated and present an overview of when these problems can be decided in polynomial time if K and L are given by nondeterministic automata.

COMPLEXITY IN UNION-FREE REGULAR LANGUAGES

We continue the investigation of union-free regular languages that are described by regular expressions without the union operation. We also define deterministic union-free languages as languages accepted by one-cycle-free-path deterministic finite automata, and show that they are properly included in the class of union-free languages. We prove that (deterministic) union-freeness of languages does not accelerate regular operations, except for the reversal in the nondeterministic case.

Coordination control of discrete-event systems revisited

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.

Synthesis of Controllable and Normal Sublanguages for Discrete-Event Systems using a Coordinator

Synthesis of normal or controllable and normal sublanguages of global specification languages without computation of the global modular plant is a difficult problem. In this paper, these sublanguages are computed using a coordinator. We recall the notion of conditional controllability, introduce a notion of conditional normality, and prove necessary and sufficient conditions where such a computation is possible. Specifically, we show that conditionally controllable and conditionally normal languages computed by our method are controllable and normal with respect to the global plant. The optimality (supremality) of the resulting languages is also discussed.

Multilevel coordination control of modular DES

A top-down approach to multilevel coordination control is presented along with the corresponding notions of conditional decomposability and conditional controllability. The multilevel structure makes the approach computationally more efficient in comparison with the approach of one central coordinator since fewer events need to be communicated among subsystems. Necessary and sufficient conditions are stated for a specification to be achieved by the proposed top-down approach.

Complexity in union-free regular languages

We continue the investigation of union-free regular languages that are described by regular expressions without the union operation. We also define deterministic union-free languages as languages recognized by one-cycle-free-path deterministic finite automata, and show that they are properly included in the class of union-free languages. We prove that (deterministic) union-freeness of languages does not accelerate regular operations, except for the reversal in the nondeterministic case.

On a structural property in the state complexity of projected regular languages

A transition is unobservable if it is labeled by a symbol removed by a projection. The present paper investigates a new structural property of incomplete deterministic finite automata-a number of states incident with an unobservable transition-and its effect on the state complexity of projected regular languages. We show that the known upper bound can be met only by automata with one unobservable transition (up to unobservable multi-transitions). We improve this upper bound by taking into consideration the structural property of minimal incomplete automata, and prove the tightness of new upper bounds. Special attention is focused on the case of finite languages. The paper also presents and discusses several fundamental problems which are still open.