Computation of controllable and coobservable sublanguages in decentralized supervisory control via communication

Abstract

In decentralized supervisory control, several local supervisors cooperate to accomplish a common goal (specification). Controllability and coobservability are the key conditions to achieve a specification in the controlled system. We construct a controllable and coobservable sublanguage of the specification by using additional communications between supervisors. Namely, we extend observable events of local supervisors via communication and apply a fully decentralized computation of local supervisors. Coobservability is then guaranteed by construction. Sufficient conditions to achieve the centralized optimal solution are discussed. Our approach can be used for both prefix-closed and non-prefix-closed specifications.

Complexity of Infimal Observable Superlanguages

“…Another motivation and the importance of infimal superlanguages have been discussed in the fundamental book on supervisory control theory [6]. We have further illustrated its relevance to decentralized supervisory control with communication [7] and to coordination control [8]. We refer the reader to these papers for more details and examples.…”

“…There are examples in modular and decentralized control showing evidence that supremal sublanguages do not always suffice to achieve the best (optimal) solution and that the optimal solution may be achieved if infimal superlanguages are involved. The examples show evidence that the combination of supremal sublanguages and infimal superlanguages help achieve optimality if it is not achievable by supremal sublanguages alone [7], [8]. Therefore our interest in infimal prefix-closed, controllable and observable superlanguages.…”

Supervisory Control for Stabilization under Multiple Local Average Payoff Constraints

“…Supervisory control theory has been comprehensively discussed in various DES models, among which automata and Petri nets are most commonly used. Many mechanisms of supervisory control have been developed so far: control under partial observation [31], [32], networked control [24], [35], decentralized control [13], [30], control of timed DES [21], [34], learning based control [28], [33], compositional control [6], [18], robust control [1], [17], online control [15], [22], supervisory control for DES with nondeterministic specifications [25], [29], to name a few. The conventional framework of qualitative supervisory control is also extended to quantitative settings, where supervisors are designed to achieve some measures defined over states and transitions.…”