Jan Komenda

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 Discrete-Event Systems with Partial Observations Using Coalgebra and Coinduction

Control of discrete-event systems with partial observations is treated by concepts and results of coalgebra and coinduction. Coalgebra is part of abstract algebra and enables a generalization of the computer science concept of bisimulation. It can be applied to automata theory and then provides a powerful algebraic tool to treat problems of supervisory control. A framework for control of discrete-event systems with partial observations is formulated in terms of coalgebra. The contributions to control theory are besides the framework, algorithms for supremal normal and supremal normal and controllable sublanguages of the plant.

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.

Supervisory control of modular systems with global specification languages

The paper presents sufficient conditions for modular (supervisory) control synthesis to equal global control synthesis. In modular control synthesis a supervisory control is synthesized for each module separately and the supervisory control consists of the parallel composition of the modular supervisory controls. The general case of the specification that is indecomposable and not necessarily contained in the plant language, which is often the case in practice, is considered. The usual assumption that all shared events are controllable is relaxed by introducing two new structural conditions relying on the global mutual controllability condition. The novel concept used as a sufficient structural condition is strong global mutual controllability. The main result uses a weaker condition called global mutual controllability together with local consistency of the specification. An example illustrates the approach.

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.

Modular Control of Discrete-Event Systems With Coalgebra

Modular supervisory control of discrete-event systems, where the overall system is a synchronous (parallel) product of subsystems, is considered. The main results of this paper are formulations of sufficient conditions for the compatibility between the synchronous product and various operations stemming from supervisory control as supervised product and supremal controllable sublanguages. These results are generalized to the case of modules with partial observations: e.g., modular computation of supremal normal sublanguages is studied. Coalgebraic techniques based on the coinduction proof principle are used in our main results. Sufficient conditions are derived for modular to equal global control synthesis. An algorithmic procedure for checking the new conditions is proposed and the computational benefit of the modular approach is discussed and illustrated by comparing the time complexity of modular and monolithic computation.

Modular Supervisory Control with General Indecomposable Specification Languages

Modular supervisory control of discrete-event systems (DES), where the global DES is composed of local components that run concurrently, is considered. For supervisory control of large-scale modular DES the possibility of performing control-related computations locally (in components) is of utmost importance to computational complexity. Recently we have treated the case, where the specification language is decomposable into local specification languages and is included in the (global) plant language. In this paper the case of general specification languages that are neither necessarily decomposable nor contained in the global plant language is studied. Sufficient conditions are found under which any manipulation with the global plant is avoided for the computation of supremal controllable sublanguages of (global) indecomposable specification languages.

Supervisory Control of (max,+) Automata: A Behavioral Approach

A behavioral framework for control of (max,+) automata is proposed. It is based on behaviors (formal power series) and a generalized version of the Hadamard product, which is the behavior of a generalized tensor product of the plant and controller (max,+) automata in their linear representations. In the tensor product and the Hadamard product, the uncontrollable events that can neither be disabled nor delayed are distinguished. Supervisory control of (max,+) automata is then studied using residuation theory applied to our generalization of the Hadamard product of formal power series. This yields a notion of controllability of formal power series as well as (max,+)-counterparts of supremal controllable languages. Finally, rationality as an equivalent condition to realizability of the resulting controller series is discussed together with hints on future use of this approach.

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.