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

Multi-resolution fault diagnosis in discrete-event systems

In this thesis, a framework for multi-resolution fault diagnosis in discrete-event systems (DES) is introduced. Here a sequence of plant models, with increasing resolution, are used in fault diagnosis and the range of possible diagnosis is narrowed down step by step, until the failure node is isolated. In this way, the original problem of fault diagnosis is replaced by a sequence of smaller problems. The plant models used at each step of diagnosis are abstractions of the original plant model. We propose to use model reduction through the solutions of the Relational Coarsest Partition problem to obtain these abstractions. For each diagnosis step, minimal sensor sets are chosen to have a coarser output map, and hence, to improve the efficiency of model reduction. In this thesis, a polynomial algorithm is proposed that verifies failure diagnosability by examining the distinguishability of two plant (normal/faulty) conditions at a time. A procedure is presented that finds minimal sensor sets, referred to as minimal distinguishes for distinguishability of one condition from another. A polynomial procedure is introduced that combines minimal distinguishers to obtain a minimal sensor set for fault diagnosis. The proposed method reduces the computational complexity of sensor selection. A benefit of using minimal distinguishers is that their computation maybe speeded up using expert knowledge. The proposed method for sensor selection is particularly suitable for multi-resolution diagnosis since it permits some of the results of computations, performed for sensor selection at the lowest (finest) level of multi-resolution diagnosis to be reduced at higher levels. This feature is particularly useful in reducing the computations necessary for online reconfiguration of the multi-resolution diagnosis system. An important procedure used in sensor selection is testing diagnosability. In this thesis, a new procedure for testing diagnosability in timed DES is introduced based on the relatively timing of plant output sequence. It is shown through example that the proposed test maybe executed with significantly fewer computations compared to tests developed for untimed models and adapted for timed systems. Furthermore, two new sets of sufficient conditions are provided under which diagnoser design and diagnosability tests based on relative timing of output sequence can be performed efficientl

Combining advantages from parameters in modeling and control of discrete event systems

Although Finite-State Automata (FSA) have been successfully used in modeling and control of Discrete Event Systems (DESs), they are limited to represent complex and advanced features of DESs, such as context recognition and switching. The literature has suggested that a FSA can nevertheless be enriched with parameters properly collected from the modeled system, so that this favors design and control. A parameter can be embedded either on transitions or states. However, each approach is structured within a specific framework, so that their comparison and integration are not straightforward and they may lead to different control solutions, modeled, computed and implemented using distinct strategies. In this paper, we show how to combine advantages from parameters in modeling and control of DESs. Each approach is structured and their advantages are identified and exemplified. Then, we propose a conversion method that allows to translate a design-friendly model into a synthesis-efficient structure. Examples illustrate the approach.CNPq, under grant number 402145/2016-0, 09, Araucaria Foundation, CAPES, and FINEP, and partially supported by ERDF - The European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation - COMPETE 2020 Programme, and by National Funds through FCT - Fundação para a Ciência e a Tecnologia, within project POCI- ˆ 01-0145-FEDER-030947 (KLEE

Structuring Multilevel Discrete-Event Systems With Dependence Structure Matrices

Despite the correct-by-construction property, one of the major drawbacks of supervisory control synthesis is state-space explosion. Several approaches have been proposed to overcome this computational difficulty, such as modular, hierarchical, decentralized, and multilevel supervisory control synthesis. Unfortunately, the modeler needs to provide additional information about the system's structure or controller's structure as input for most of these nonmonolithic synthesis procedures. Multilevel synthesis assumes that the system is provided in a tree-structured format, which may resemble a system decomposition. In this paper, we present a systematic approach to transform a set of plant models and a set of requirement models provided as extended finite automata into a tree-structured multilevel discrete-event system to which multilevel supervisory control synthesis can be applied. By analyzing the dependencies between the plants and the requirements using dependence structure matrix techniques, a multilevel clustering can be calculated. With the modeling framework of extended finite automata, plant models and requirements depend on each other when they share events or variables. We report on experimental results of applying the algorithm's implementation on several models available in the literature to assess the applicability of the proposed method. The benefit of multilevel synthesis based on the calculated clustering is significant for most large-scale systems

SYNTHESIS EQUIVALENCE OF TRIPLES

This working paper describes a framework for compositional supervisor synthesis, which is applicable to all discrete event systems modelled as a set of deterministic automata. Compositional synthesis exploits the modular structure of the input model, and therefore works best for models consisting of a large number of small automata. The state-space explosion is mitigated by the use of abstraction to simplify individual components, and the property of synthesis equivalence guarantees that the final synthesis result is the same as it would have been for the non-abstracted model. The working paper describes synthesis equivalent abstractions and shows their use in an algorithm to efficiently compute supervisors. The algorithm has been implemented in the DES software tool Supremica and successfully computes nonblocking modular supervisors, even for systems with more than 1014 reachable states, in less than 30 seconds

Synthesis of least restrictive controllable supervisors for extended finite-state machines with variable abstraction

This paper presents an algorithm that combines modular synthesis for extended finite-state machines (EFSM) with abstraction of variables by symbolic manipulation, in order to compute least restrictive controllable supervisors. Given a modular EFSM system consisting of several components, the proposed algorithm synthesises a separate supervisor for each specification component. To synthesise each supervisor, the algorithm iteratively selects components (plants and variables) from a synchronous composition until a least restrictive controllable solution is obtained. This improves on previous results of the authors where abstraction is only performed by the selection of components and not variables. The paper explains the theory of EFSM synthesis and abstraction and its algorithms. An example of a flexible manufacturing system illustrates how the proposed algorithm works to compute a modular supervisor

Framework and proofs for synthesis of least restrictive controllable supervisors for extended finite-state machines with variable abstraction

This working paper presents an algorithm that combines modular synthesis for extended finite-state machines (EFSM) with abstraction of variables by symbolic manipulation, in order to compute least restrictive controllable supervisors. Given a modular EFSM system consisting of several components, the proposed algorithm synthesises a separate supervisor for each specification component. To synthesise each supervisor, the algorithm iteratively selects components (plants and variables) from a synchronous composition until a least restrictive controllable solution is obtained. This improves on previous results of the authors where abstraction is only performed by the selection of components and not variables. The working paper explains the theory of EFSM synthesis and abstraction and includes formal proofs of all results. An example of a flexible manufacturing system illustrates how the proposed algorithm works to compute a modular supervisor

On Compositional Approaches for Discrete Event Systems Verification and Synthesis

Over the past decades, human dependability on technical devices has rapidly increased.Many activities of such devices can be described by sequences of events,where the occurrence of an event causes the system to go from one state to another.This is elegantly modelled by state machines. Systems that are modelledin this way are referred to as discrete event systems. Usually, these systems arehighly complex, and appear in settings that are safety critical, where small failuresmay result in huge financial and/or human losses. Having a control functionis one way to guarantee system correctness.The work presented in this thesis concerns verification and synthesis of suchsystems using the supervisory control theory proposed by Ramadge and Wonham. Supervisory control theory provides a general framework to automaticallycalculate control functions for discrete event systems. Given a model of thesystem, the plant to be controlled, and a specification of the desired behaviour,it is possible to automatically compute, i.e. synthesise, a supervisor that ensuresthat the specification is satisfied.Usually, systems are modular and consist of several components interactingwith each other. Calculating a supervisor for such a system in the straightforwardway involves constructing the complete model of the considered system, whichmay lead to the inherent complexity problem known as the state-space explosionproblem. This problem occurs as the number of states grows exponentially withthe number of components, which makes it intractable to examine the globalstates of a system due to lack of memory and time.One way to alleviate the state-space explosion problem is to use a compositionalapproach. A compositional approach exploits the modular structure of asystem to reduce the size of the model. This thesis mainly focuses on developingabstraction methods for the compositional approach in a way that the finalverification and synthesis results are the same as it would have been for the nonabstractedsystem. The algorithms have been implemented in the discrete eventsystem software tool Supremica and have been applied to verify and computememory efficient supervisors for several large industrial models