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

Decentralized supervisory control of reactive discrete-event systems

In this thesis we propose to apply Ramadge-Wonham supervisory control theory to Reactive Discrete-Event Systems (RDES). A reactive system continually interacts with its environment at the speed dictated by the latter. We will first present our decentralized RDES architecture, which is based on Input/Output (I/O) automata model. After introducing safety and progress, we define the corresponding centralized and decentralized supervisory control problems concerning both safety and progress. We explain through examples why the existing results in supervisory control theory cannot be directly applied. Substitute sufficient and necessary conditions for the existence of decentralized solutions are given. In the special case where only safety is considered, we also study centralized and decentralized supervisory control problems, and present more straightforward sufficient and necessary conditions for the existence of their solutions. An example is presented to illustrate how decentralized RDES are modeled, how decentralized components co-operate with each other, and how the revised decentralized supervisory control theory can be applied to the study of RDES

Robust decentralized supervisory control of discrete-event systems

In this thesis we study robust supervisory control of discrete event systems in two different settings. First, we consider the problem of synthesizing a set of decentralized supervisors when the precise model of the plant is not known, but it is known that it is among a finite set of plant models. To tackle this problem, we form the union of all possible behaviors and construct an appropriate specification, from the given set of specifications, and solve the conventional decentralized supervisory control associated with it. We also prove that the given robust problem has a solution if and only if this conventional decentralized supervisory control problem has a solution. In another setting, we investigate the problem of synthesizing a set of communicating supervisors in the presence of delay in communication channels, and call it Unbounded Communication Delay Robust Supervisory Control problem (UCDR-SC problem). In this problem, We assume that delay is unbounded but it is finite, meaning that any message sent from a local supervisor will be received by any other local supervisors after a finite but unknown delay. To solve this problem, we redefine the supervisory decision making rules, introduce a new language property called unbounded-communication-delay-robust (UCDR), and present a set of conditions on the specification of the problem. We also show that the new class of languages that is the solution to this problem has some interesting relations with other observational languages

Observability and Decentralized Control of Fuzzy Discrete Event Systems

Fuzzy discrete event systems as a generalization of (crisp) discrete event systems have been introduced in order that it is possible to effectively represent uncertainty, imprecision, and vagueness arising from the dynamic of systems. A fuzzy discrete event system has been modelled by a fuzzy automaton; its behavior is described in terms of the fuzzy language generated by the automaton. In this paper, we are concerned with the supervisory control problem for fuzzy discrete event systems with partial observation. Observability, normality, and co-observability of crisp languages are extended to fuzzy languages. It is shown that the observability, together with controllability, of the desired fuzzy language is a necessary and sufficient condition for the existence of a partially observable fuzzy supervisor. When a decentralized solution is desired, it is proved that there exist local fuzzy supervisors if and only if the fuzzy language to be synthesized is controllable and co-observable. Moreover, the infimal controllable and observable fuzzy superlanguage, and the supremal controllable and normal fuzzy sublanguage are also discussed. Simple examples are provided to illustrate the theoretical development.Comment: 14 pages, 1 figure. to be published in the IEEE Transactions on Fuzzy System

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

Supervisory control of fuzzy discrete event systems with applications to mobile robotics

Fuzzy Discrete Event Systems (FDES) were proposed in the literature for modeling and control of a class of event driven and asynchronous dynamical systems that are affected by deterministic uncertainties and vagueness on their representations. In contrast to classical crisp Discrete Event Systems (DES), which have been explored to a sufficient extent in the past, an in-depth study of FDES is yet to be performed, and their feasible real-time application areas need to be further identified. This research work intends to address the supervisory control problem of FDES broadly, while formulating new knowledge in the area. Moreover, it examines the possible applications of these developments in the behavior-based mobile robotics domain. An FDES-based supervisory control framework to facilitate the behavior-based control of a mobile robot is developed at first. The proposed approach is modular in nature and supports behavior integration without making state explosion. Then, this architecture is implemented in simulation as well as in real-time on a mobile robot moving in unstructured environments, and the feasibility of the approach is validated. A general decentralized supervisory control theory of FDES is then established for better information association and ambiguity management in large-scale and distributed systems, while providing less complexity of control computation. Furthermore, using the proposed architecture, simulation and real-time experiments of a tightly-coupled multi-robot object manipulation task are performed. The results are compared with centralized FDES-based and decentralized DES-based approaches. -- A decentralized modular supervisory control theory of FDES is then established for complex systems having a number of modules that are concurrently operating and also containing multiple interactions. -- Finally, a hierarchical supervisory control theory of FDES is established to resolve the control complexity of a large-scale compound system by modularizing the system vertically and assigning multi-level supervisor hierarchies. As a proof-of-concept example to the established theory, a mobile robot navigation problem is discussed. This research work will contribute to the literature by developing novel knowledge and related theories in the areas of decentralized, modular and hierarchical supervisory control of FDES. It also investigates the applicability of these contributions in the mobile robotics arena

Quantitatively-Optimal Communication Protocols for Decentralized Supervisory Control of Discrete-Event Systems

In this thesis, decentralized supervisory control problems which cannot be solved without some communication among the controllers are studied. Recent work has focused on finding minimal communication sets (events or state information) required to satisfy the specifications. A quantitative analysis for the decentralized supervisory control and communication problem is pursued through which an optimal communication strategy is obtained. Finding an optimal strategy for a controller in the decentralized control setting is challenging because the best strategy depends on the choices of other controllers, all of whom are also trying to optimize their own strategies. A locally-optimal strategy is one that minimizes the cost of the communication protocol for each controller. Two important solution concepts in game theory, namely Nash equilibrium and Pareto optimality, are used to analyze optimal interactions in multi-agent systems. These concepts are adapted for the decentralized supervisory control and communication problem. A communication protocol may help to realize the exact control solution in decentralized supervisory control problem; however, the cost may be high. In certain circumstances, it can be advantageous, from a cost perspective, to reduce communication, but incur a penalty for synthesizing an approximate control solution. An exploration of the trade-off between the cost and accuracy of a decentralized discrete-event control solution with synchronously communicating controllers in a multi-objective optimization problem is presented. A widely-used evolutionary algorithm (NSGA-II) is adapted to examine the set of Pareto-optimal solutions that arise for this family of decentralized discrete-event systems (DES). The decentralized control problem is synthesized first by considering synchronous communication among the controllers. In practice, there are non-negligible delays in communication channels which lead to undesirable effects on controller decisions. Recent work on modeling communication delay between controllers only considers the case when all observations are communicated. When this condition is relaxed, it may still be possible to formulate communicating decentralized controllers that can solve the control problem with reduced communications. Instead of synthesizing reduced communication protocols under bounded delay, a procedure is developed for testing protocols designed for synchronous communications (where not all observations are communicated) for their robustness under conditions when only an upper bound for channel delay is known. Finally a decentralized discrete-event control problem is defined in timed DES (TDES) with known upper-bound for communication delay. It is shown that the TDES control problem with bounded delay communication can be converted to an equivalent problem with no delay in communication. The latter problem can be solved using the algorithms proposed for untimed DES with synchronous communication