Control Theory Of Discrete Event Systems Research Articles

Control of Black-Box Embedded Systems by Integrating Automaton Learning and Supervisory Control Theory of Discrete-Event Systems

The paper presents an approach to the control of black-box embedded systems by integrating automaton learning and supervisory control theory (SCT) of discrete-event systems (DES), where automaton models of both the system and requirements are unavailable or hard to obtain. First, the system is tested against the requirements. If all the requirements are satisfied, no supervisor is needed and the process terminates. Otherwise, a supervisor is synthesized to enforce the system to satisfy the requirements. To apply SCT and automaton learning technologies efficiently, the system is abstracted to be a finite-discrete model. Then, a $C^{*}$ learning algorithm is proposed based on the classical $L^{*}$ algorithm to infer a Moore automaton describing both the behavior of the system and the conjunctive behavior of the system and the requirements. Subsequently, a supervisor for the system is derived from the learned Moore automaton and patched on the system. Finally, the controlled system is tested again to check the correctness of the supervisor. If the requirements are still not satisfied, a larger Moore automaton is learned and a refined supervisor is synthesized. The whole process iterates until the requirements hold in the controlled system. The effectiveness of the proposed approach is manifested through two realistic case studies. Note to Practitioners —Supervisory control theory of DES can synthesize maximally permissive supervisory controllers to ensure the correctness of software-controlled processes. The application of supervisory control theory relies on automaton models of the plant and specifications; however, the required models are often unavailable and difficult to obtain for black-box embedded systems. Automaton learning is an effective method for inferring models of black-box systems. This paper integrates the two technologies so that the supervisory control theory is applicable to the development of black-box embedded software systems. The proposed approach is implemented in a toolchain that connects automaton learning algorithms, SCT, and testing algorithms via scripts. The obtained supervisor is implemented as a software patch to monitor and control the original system online.

Control of Flexible Manufacturing Systems under model uncertainty using Supervisory Control Theory and evolutionary computation schedule synthesis

A new approach for the problem of optimal task scheduling in flexible manufacturing systems is proposed in this work, as a combination of metaheuristic optimization techniques with the supervisory control theory of discrete-event systems. A specific encoding, the word-shuffling encoding, which avoids the generation of a large number of infeasible sequences, is employed. A metaheuristic method based on a Variable Neighborhood Search is then built using such an encoding. The optimization algorithm performs the search for the optimal schedules, while the supervisory control has the role of codifying all the problem constraints, allowing an efficient feasibility correction procedure, and avoiding schedules that are sensitive to uncertainties in the execution times associated with the plant operation. In this way, the proposed methodology achieves a system performance which is typical from model-predictive scheduling, combined with the robustness which is required from a structural control.

Cooperation of agents in complex systems based on supervision

Abstract Complex systems consist of many cooperating devices. To have a transparent view on the system structure, as well as on the structural interconnections and cooperation of the subsystems, it is useful to synthesize the complex systems systematically in a prescribed order, even in analytical terms (if possible). The supervision of the subsystems seems to be a very suitable approach to accomplish these demands, and consequently it makes the complex systems diagnostics easier. The substantial agents (i.e., the agents of material nature − e.g., devices like particular production lines, robots, numerically controlled machines, etc.) can be coordinated and forced to cooperation by means of efficiently synthesized supervisors. The cooperation process has the character of DES (Discrete-Event Systems), because any system (including continuous systems), has minimally two discrete states - idle and working. DES control theory can be successfully utilized in supervisor synthesis. There are several approaches to modeling the agents and the process of supervisor synthesis. The Petri net-based approach is one of them. Place/Transition Petri Nets (P/T PN) are used here for modeling the behaviour of particular agents, as well as in the computational parocess used for the supervisor synthesis. Two main methods of the P/T PN-based supervision will be used, namely (i) the supervision based on the place invariants (P-invariants) of P/T PN, utilizing only the state vector during the supervisor synthesis, and (ii) the extended supervision utilizing not only the state vector, but also the control vector and Parikh’s vector. The efficiency of the proposed approach is illustrated in a case study.

Modal Specifications for the Control Theory of Discrete Event Systems

We propose a logical framework for the control theory of reactive systems modeled by discrete event systems. The logic is the conjunctive nu-calculus, an expressive fragment of the powerful mu-calculus. Conjunctive nu-calculus possesses an alternative presentation based on modal specifications, with simple graphical representations. We exploit modal specification to specify and to solve the basic centralized control problem: our class of control objectives strictly subsumes the class of regular languages, normally used in the classic control theory of discrete-event systems, but the existence of maximally permissive solutions is however preserved.

On the Computation of Observers in Discrete-Event Systems

The concept of observer was introduced in previous work by the authors on a hierarchical control theory of discrete-event systems (DES). It was shown that the observer property of the “causal reporter” map, which in this theory models information flow in a hierarchical DES, plays a role in ensuring that a nonblocking supervisor at a given level of a hierarchy does not cause blocking in the level below. In this paper, we investigate the following problem: Given a causal reporter map that is not an observer, how can we design an observer by modifying this map? In case the latter is represented by a finite Mealy automaton, an effective computational algorithm is developed for computing an observer with the coarsest possible equivalence kernel that is finer than that of the given map. Three examples are provided for illustration.

Discrete approximation and supervisory control of continuous systems

Addresses the following hybrid control problem: a continuous plant (its state evolving in Euclidean space) is to be controlled via symbolic output feedback-both measurement and control signal "live" on finite sets of symbols. We adopt the following approach: the hybrid problem is first translated into a purely discrete problem by approximating the continuous plant model by a (nondeterministic) finite-state machine. By taking into account past measurement and control symbols, approximation accuracy can be improved and adjusted to the specification requirements. Supervisory control theory for discrete-event systems (DES) is then applied to find the optimal controller which enforces the specifications. As the behavior of the approximating automaton is guaranteed to contain the behavior of the underlying continuous plant model, the controller also forces the latter to obey the specifications.

Two formal methods for the synthesis of discrete event systems

The design of discrete event systems (DES) is based mainly on either analysis or synthesis approaches. In the synthesis approach, the design process starts from high level requirements which are then automatically refined to obtain lower abstraction levels. In this paper, we begin by introducing the two design approaches and defining the synthesis problem in DESs, and in protocols in particular. Then, we survey and assess some existing protocol synthesis methods. Then, we present two novel formal and systematic methods we have developed for the synthesis of DESs. The first method is used for the design of distributed systems which must satisfy some temporal constraints. The second method takes into account concepts such as controllability and observability, which are used in the control theory of DESs. Finally, we conclude and propose some future works.

Specifying goal-oriented network management systems

Work aimed at describing the most adequate framework for the design of real-time network management systems and the associated interfaces for open systems is discussed. This framework has been developed by integrating three mathematical techniques: automatic control theory for discrete-event systems, which provides the architectural framework and is the unifying theme that holds together the various parts of the system; predicate-transition Petri net theory, which provides the representation framework; and logic programming (Prolog), which provides the description framework. The ways in which management/user and interface requirements are constructed using this system design framework, which is being developed in the context of real applications, are described. >