A decidable class of problems for control under partial observation

Abstract

The commonly accepted control theory for discrete event systems, due to Ramadge and Wonham [13], followed by several other [17,4], has been more recently extended to temporal logic specifications [8,2,14]. Control consists in supervising a plant to guarantee some desired behavior, called control objectives; the objectives are standard properties such as non-blocking, safety, temporal logic definable behaviors, etc. Concerning the nature of the supervision, it is natural and standard to suppose a partial observation of the plant, as information on it moves and states is incomplete; we then talk about control under partial observation (see [11]). In this paper, we adapt the logical approach of [14] to specify control under partial observation. This approach is based on quantification over atomic propositions of the mu-calculus of [7], called the quantified mu-calculus. We prove the decidability of controller synthesis when the specification is a nested observational formula: the construction of controllers relies on the generalizations of the automata quotient of [2] and the automata projection of [14]. An immediate important corollary is the synthesis of maximally permissive controllers under partial observation for mu-calculus definable control objectives. To our knowledge, maximal permissiveness of controllers has never been properly answered before: permissiveness is manageable in the regular languages framework [10], but becomes intricate when branching-time objectives are considered. The few results of the literature are [14] which concern control problems with full observation, and [8,2] which do not take maximal permissiveness into account. The paper is organized as follows: Sec.1 introduces the quantified mu-calculus and show its adequacy to control specification ; Sec.2 is dedicated to the control synthesis for the decidable fragment of the logic.

DOI: 10.1016/j.ipl.2005.04.011

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Cite this paper

@article{Pinchinat2005ADC, title={A decidable class of problems for control under partial observation}, author={Sophie Pinchinat and St{\'e}phane Riedweg}, journal={Inf. Process. Lett.}, year={2005}, volume={95}, pages={454-460} }