Uma abordagem local para o controle supervisório modular de sistemas a eventos discretos temporizados

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia de Automação e Sistemas, Florianópolis, 2014.Nesta dissertação, propomos uma abordagem para a síntese local de supervisores modulares no contexto de sistemas a eventos discretos temporizados. O objetivo é reduzir o custo computacional na aplicação da teoria de controle supervisório a essa classe de sistemas, haja vista a dificuldade imposta pela explosão no número de estados dos modelos em sistemas de grande porte. Em grande parte dos problemas complexos envolvendo sistemas temporizados, a planta a ser controlada é composta de subsistemas que operam de maneira assíncrona a menos do compartilhamento de um relógio global. Ademais, o comportamento desejado é normalmente colocado na forma de especificações de controle elementares, cada uma das quais visa sincronizar e restringir o comportamento de apenas alguns dos subsistemas da planta. A ideia da metodologia de controle aqui apresentada é explorar tanto a modularidade das especificações quanto a do próprio sistema. Nossos supervisores são calculados com base em modelos locais, construídos pela agregação dos subsistemas que são afetados por cada especificação. Isso leva a módulos de controle nos quais a ação dos supervisores é relativamente simples, baseada apenas em informações locais, o que facilita sua compreensão, implementação e modificação. Apresentamos condições necessárias e suficientes sob as quais a ação conjunta dos supervisores locais leva o sistema a um comportamento global não bloqueante e que cumpre as especificações de forma ótima (minimamente restritiva). Mostramos, ainda, que a abordagem proposta reduz o custo computacional quando comparada a outras existentes. Por fim, um exemplo de interesse prático e com rígidas restrições temporais é resolvido, ilustrando a aplicabilidade da metodologia proposta.Abstract : In this thesis, an approach is proposed for the local synthesis of modular supervisors in the context of timed discrete-event systems. The objective is to reduce computational costs for the application of timed supervisory control, in face of the hindrances imposed by state explosion in the models of large scale systems. In a wide variety of complex problems involving timing issues, the plant to be controlled is composed of subsystems that work asynchronously except for the sharing of a global clock. Moreover, the desired behavior for the plant is usually represented by a number of elementary control specifications, each of which attempts to restrict and synchronize the behavior of only some of the system's components. The idea of our control methodology is to explore the modularity of both the specifications and the system itself. Our supervisors are designed over local models, which are obtained by aggregating the subsystems affected by each specification. This results in control modules with relatively simple supervisory actions, based only on local information, which makes the supervisors easier to comprehend, implement, and modify. We present necessary and suficient conditions under which the concurrent action of the local supervisors leads the system to a nonblocking global behavior that complies with the specifications in an optimal (minimally restrictive) way. We also show that the proposed strategy reduces computational efforts in comparison with existing ones. Finally, a practical problem with critical time restrictions is solved to exemplify an application of the proposed control methodology

Optimalsteuerung zeitbehafteter Synchronisationsgraphen mit Ressourcenkonkurrenz und Aktualisierung von Referenzsignalen

Timed event graphs (TEGs) are a subclass of timed Petri nets that model synchronization and delay phenomena, but not conflict or choice. We consider a scenario where a number of TEGs share one or several resources and are subject to changes in their output-reference signals. Because of resource sharing, the resulting overall discrete event system is not a TEG. We propose a formal method to determine the optimal control input for such systems, where optimality is in the sense of the widely adopted just-in-time criterion. Our approach is based on a prespecified priority policy for the TEG components of the overall system. It builds on existing control theory for TEGs, which exploits the fact that, in a suitable mathematical framework (idempotent semirings such as the max-plus or the min-plus algebra), the temporal evolution of TEGs can be described by a set of linear time-invariant equations.Zeitbehaftete Synchronisationsgraphen (ZSGen) bilden eine spezielle Klasse zeitbehafteteter Petri-Netze. Sie können Synchronisations- und Verzögerungsphänomene modellieren, nicht aber Konflikte. Wir untersuchen ein Szenario, in dem sich mehrere ZSGen eine oder mehrere Ressourcen teilen und die Referenzsignale der ZSGen unvorhersehbaren Änderungen unterworfen sind. Da die beteiligten ZSGen um Ressourcen konkurrieren, ist das Gesamtsystem kein ZSG. Wir beschreiben eine formale Vorgehensweise zur Bestimmung des im just-in-time Sinne optimalen Stellsignals für dieses Gesamtsystem. Unser Ansatz basiert auf einer vorab festgelegten Priorisierung der einzelnen ZSGen. Er baut auf der existierenden Regelungstheorie für ZSGen auf und nutzt die Tatsache, dass sich die zeitliche Entwicklung von ZSGen in einem geeigneten mathematischen Rahmen (idempotente Halbringe wie beispielsweise die max-plus- oder die min-plus-Algebra) durch lineare zeitinvariante Gleichungen beschreiben lässt

The Hadamard product, its residual, and its dual residual in the dioid of counters: algorithms and implementation in C++

This report presents the algorithms for computing the Hadamard product, its residual, and its dual residual between formal power series in the dioid of counters. The algorithms have been implemented in the C++ toolbox ETVO ((Event|Time)-Variant Operators). After proving the correctness of the algorithms, we present a user guide for the C++ implementation.Comment: 26 pages, 2 figures, technical repor

A Novel Approach for the Modeling and Control of Timed Event Graphs with Partial Synchronization

International audienceTimed event graphs (TEGs) are a subclass of timed Petri nets whose dynamics is governed by standard synchronization, i. e., a transition is enabled to fire a certain time after the firing of some other transition(s) and is never disabled by the firing of other transitions. Partial synchronization (PS) imposes an additional condition: a partially synchronized transition can only fire within certain time windows determined by an external signal. Considering TEGs with PS allows to express time-varying behavior, which is manifested in several scenarios of practical relevance. We propose an original approach to model and control TEGs with PS, developed entirely within the domain of the dioid of counters, on which a well-consolidated control theory is available. Additionally, we show that our method can be combined with recent results and applied to the optimal control of TEGs with both PS and resource-sharing phenomena

Optimal control of timed event graphs with resource sharing and output-reference update

International audienceZusammenfassung: Zeitbehaftete Synchronisationsgra-phen (ZSGen) bilden eine spezielle Klasse zeitbehafteteter Petri-Netze. Sie können Synchronisations-und Verzöge-rungsphänomene modellieren, nicht aber Konflikte. Wir untersuchen ein Szenario, in dem sich mehrere ZSGen eine oder mehrere Ressourcen teilen und die Referenzsignale der ZSGen unvorhersehbaren Änderungen unterworfen sind. Da die beteiligten ZSGen um Ressourcen konkur-rieren, ist das Gesamtsystem kein ZSG. Wir beschreiben eine formale Vorgehensweise zur Bestimmung des im just-in-time Sinne optimalen Stellsignals für dieses Gesamt-system. Unser Ansatz basiert auf einer vorab festgelegten Priorisierung der einzelnen ZSGen. Er baut auf der exis-tierenden Regelungstheorie für ZSGen auf und nutzt die Tatsache, dass sich die zeitliche Entwicklung von ZSGen in einem geeigneten mathematischen Rahmen (idempo-tente Halbringe wie beispielsweise die max-plus-oder die min-plus-Algebra) durch lineare zeitinvariante Gleichun-gen beschreiben lässt.Timed event graphs (TEGs) are a subclass of timed Petri nets that model synchronization and delay phenomena, but not conflict or choice. We consider a scenario where a number of TEGs share one or several resources and are subject to changes in their output-reference signals. Because of resource sharing, the resulting overall discrete event system is not a TEG. We propose a formal method to determine the optimal control input for such systems, where optimality is in the sense of the widely adopted just-in-time criterion. Our approach is based on a prespecified priority policy for the TEG components of the overall system. It builds on existing control theory for TEGs, which exploits the fact that, in a suitable mathematical framework (idempotent semirings such as the max-plus or the min-plus algebra), the temporal evolution of TEGs can be described by a set of linear time-invariant equations

Optimal output feedback control of Timed Event Graphs including disturbances in a resource sharing environment

International audienceTimed Event Graphs (TEGs) constitute a subclass of timed Petri nets that model synchronization and delay phenomena, but not conflict or choice. In a suitable mathematical framework (idempotent semirings such as the min-plus algebra), the temporal evolution of TEGs can be described by a set of linear equations. Recently, a method has been proposed for the optimal control of TEGs that share one or more resources based on a prespecified priority policy.In this paper, we aim at finding a solution on how to deal with disturbances in TEGs with sharedresources, which is not possible under the current feedforward-based approaches

Implementation of procedures for optimal control of timed event graphs with resource sharing

International audienceIt is a well-known fact that the dynamics of timed event graphs (TEGs), a subclass of timed Petri nets able to model delay and synchronization phenomena, admits linear representation in dioids of formal power series. In order to model and control systems presenting resource sharing phenomena, it is useful to extend the usual set of operations between series by including the Hadamard product, its residual, and its dual residual. Until now however, the characterization of the largest set of series for which the dual residual of the Hadamard product is defined was still incomplete. Rather than being a mere theoretical dilemma, this open problem delayed the development of reliable algorithms for optimal control. In this paper, we provide the solution to the problem, and discuss the implementation of procedures for computing the Hadamard product and affine operations. Such procedures have been recently implemented on top of the C++ library ETVO. Tests are conducted to evaluate their performance in solving optimal-control problems on TEGs with resource sharing and output-reference updat