Coinduction in control of partially observed discrete-event systems

Coalgebra and coinduction provide new results and insights for the supervisory control of discrete-event systems (DES) with partial observations. In the case of full observations, coinduction has been used to define a new operation on languages called supervised product, which represents the language of the closed-loop system. The first language acts as a supervisor and the second as an open-loop system (plant). We show first that the supervised product is equal to the infimal controllable superlanguage of the supervisor's (specification) language with respect to the plant language. This can be generalized to the partial observation case, where the supervised product is shown to be equal to the infimal controllable and observable superlanguage. There are two different control laws for partially observed DES, that give the same closed-loop system if the specification is observable: permissive and antipermissive. A variation on the supervised product is presented, which corresponds to the control policy with the issue of of observability separated from the issue of controllability. It is shown to be equal to the infimal observable superlanguage. Similar idea for the antipermissive control law leads to a maximal observable sublanguage that contains the supremal normal sublanguage. We present an algorithm for its computation

Coalgebra and coinduction in decentralized supervisory control

Coalgebraic methods provide new results and insights for the supervisory control of discrete-event systems (DES). In this paper a coalgebraic framework for the decentralized control of DES is proposed. Coobservability, decomposability, and strong decomposability are described by corresponding relations and compared to each other

Coinduction in control of partially observed discrete-event systems

Coalgebra and coinduction provide new results and insights for the supervisory control of discrete-event systems (DES) with partial observations. In the case of full observations, coinduction has been used to define a new operation on languages called supervised product, which represents the language of the closed-loop system. The first language acts as a supervisor and the second as an open-loop system (plant). We show first that the supervised product is equal to the infimal controllable superlanguage of the supervisor's (specification) language with respect to the plant language. This can be generalized to the partial observation case, where the supervised product is shown to be equal to the infimal controllable and observable superlanguage. There are two different control laws for partially observed DES, that give the same closed-loop system if the specification is observable: permissive and antipermissive. A variation on the supervised product is presented, which corresponds to the control policy with the issue of of observability separated from the issue of controllability. It is shown to be equal to the infimal observable superlanguage. Similar idea for the antipermissive control law leads to a maximal observable sublanguage that contains the supremal normal sublanguage. We present an algorithm for its computation

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

Séquentialisation du comportement de réseaux de Petri temporisés

In this paper we are interested in sequentialization of formal power series with coefficients in the semiring (R ∪ {−∞}, max, +) which represent the behavior of timed Petri nets. Several approaches make it possible to derive nondeterministic (max,+) automata modeling safe timed Petri nets. Their nondeterminism is a serious drawback since determinism is a crucial property for numerous results on (max,+) automata (in particular, for applications to performance evaluation and control) and existing procedures for determinization succeed only for restrictive classes of (max,+) automata. We present a natural semi-algorithm for determinization of behaviors based on the semantics of timed Petri nets. The resulting deterministic (max,+)-automata are often infinite, but a sufficient condition is proposed to ensure that the semi-algorithm terminates and leads to a finite state deterministic (max,+)-automaton. Moreover, if the net cannot be sequentialized we propose a restriction of its logical behavior so that the sufficient condition becomes satisfied for the restricted net

Compositions of (max, +) automata

This paper presents a compositional modeling approach by means of (max, +) automata. The motivation is to be able to model a complex discrete event system by composing sub-models representing its elementary parts. A direct modeling of safe timed Petri nets using (max, +) automata is first introduced. Based on this result, two types of synchronous product of (max, +) automata are proposed to model safe timed Petri nets obtained by merging places and/or transitions in subnets. An asynchronous product is finally proposed to represent particular bounded timed Petri nets

Le produit synchrone des automates (max,+)

Une extension des automates (max,+) est étudiée dans le but de modéliser le parrallélisme (occurrence simultanée d\u27évements). Pour cela, on introduit une composition synchrone des automates (max, +) vus comme des automates temporisés. Ceci nous amène à introduire des automates (max, +) avec multi-événements qui correspondent à une classe des automates temporisés avec plusieurs horloges. Nous obtenons la formule pour le comportement de produit synchrone d\u27automates (max,+) et montrons que dans le cas général il n\u27est pas possible de définir le produit synchrone des comportement (séries formelles) sans prendre en compte leurs représentations par automates (max,+)

Application of product dioids for dead token detection in interval P-time event graphs

Linear description of interval P-time event graphs using a product idempotent semiring is proposed and applied to dead token detection. The dependence of dead token on initial condition is studied using residuation theory. Finally, the relationship with the spectral theory of matrices over product semirings is discusse