Variable abstraction and approximations in supervisory control synthesis

This paper proposes a method to simplify Extended Finite-state Automata (EFA) in such a way the least restrictive controllable supervisor is preserved. The method is based on variable abstraction, which involves the identification and removal of irrelevant variables from a model. Variable abstraction preserves controllability, and the paper shows how approximations can be used to ascertain least restrictiveness of the synthesis result. The approach has the modelling benefits of Extended Finite-state Automata, leads to optimal control solutions, and reduces the synthesis cost. An example of a manufacturing system illustrates the contributions

Efficient Symbolic Supervisory Synthesis and Guard Generation: Evaluating partitioning techniques for the state-space exploration

The supervisory control theory (SCT) is a model-based framework, which automatically synthesizes a supervisor that restricts a plant to be controlled based on specifications to be fulfilled. Two main problems, typically encountered in industrial applications, prevent SCT from having a major breakthrough. First, the supervisor which is synthesized automatically from the given plant and specification models might be incomprehensible to the users. To tackle this problem, an approach was recently presented to extract compact propositional formulae (guards) from the supervisor, represented symbolically by binary decision diagrams (BDD). These guards are then attached to the original models, which results in a modular and comprehensible representation of the supervisor. However, this approach, which computes the supervisor symbolically in the conjunctive way, might lead to another problem: the state-space explosion, because of the large number of intermediate BDD nodes during computation. To alleviate this problem, we introduce in this paper an alternative approach that is based on the disjunctive partitioning technique, including a set of selection heuristics. Then this approach is adapted to the guard generation procedure. Finally, the efficiency of the presented approach is demonstrated on a set of benchmark examples

Abstractions for nonblocking supervisory control of Extended Finite Automata

An abstraction method for Extended Finite Automata (EFAs), i.e., finite automata extended with variables, using transition projection is presented in this work. A manufacturing system modeled by EFAs is abstracted into subsystems that embody internal interacting dependencies. Synthesis and verification of subsystems are achieved through their model abstractions rather than their global model. Sufficient conditions are presented to guarantee that supervisors result in maximally permissive and nonblocking control. An examples demonstrate the computational effectiveness and practical usage of the approach

Efficiently enforcing mutual state exclusion requirements in symbolic supervisor synthesis

Given a model of an uncontrolled system and a requirement specification, a supervisory controller can be synthesized so that the system under control adheres to the requirements. There are several ways in which informal behavioral safety requirements can be formalized, one of which is using mutual state exclusion requirements. In current implementations of the supervisor synthesis algorithm, synthesis may be inefficient when mutual state exclusion requirements are used. We propose a method to efficiently enforce these requirements in supervisor synthesis. We consider symbolic supervisor synthesis, where Binary Decision Diagrams are used to represent the system. The efficiency of the proposed method is evaluated by means of an industrial and academic case study

Symbolic reachability computation using the disjunctive partitioning technique in Supervisory Control Theory

Supervisory Control Theory (SCT) is a model-based framework for automatically synthesizing a supervisor that minimally restricts the behavior of a plant such that a given specification is fulfilled. A problem, which prevents SCT from having a major breakthrough industrially, is that the supervisory synthesis often suffers from the state-space explosion problem. To alleviate this problem, a well-known strategy is to represent and explore the state-space symbolically by using Binary Decision Diagrams. Based on this principle, an efficient symbolic state-space traversal approach, depending on the disjunctive partitioning technique, is presented and the correctness of it is proved. Finally, the efficiency of the presented approach is demonstrated on a set of benchmark examples

Supervisory Control of Extended Finite Automata Using Transition Projection

A limitation of the Ramadge and Wonham (RW) framework for the supervisory control theory is the explicit state representation using finite automata, often resulting in complex and unintelligible models. Extended finite automata (EFAs), i.e., deterministic finite automata extended with variables, provide compact state representation and then make the control logic transparent through logic expressions of the variables. A challenge with this new control framework is to exploit the rich control structure established in RW's framework. This paper studies the decentralized control structure with EFAs. To reduce the computational complexity, the controller is synthesized based on model abstraction of subsystems, which means that the global model of the entire system is unnecessary. Sufficient conditions are presented to guarantee that the decentralized supervisors result in maximally permissive and nonblocking control to the entire system

On Conditional Decomposability

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 the 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 is also discussed in this paper in the general settings. It is shown that conditional decomposability is a weaker condition than nonblockingness.Comment: A few minor correction