# A Coalgebraic Approach to Supervisory Control of Partially Observed Mealy Automata

• Jun Kohjina
• Toshimitsu Ushio
• Yoshiki Kinoshita
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6859)

## Abstract

Supervisory control is a logical control method of discrete event systems introduced by Ramadge and Wonham. We propose a novel coalgebraic formulation of a supervisory control problem and design a controller called supervisor satisfying a given specification under partial observations. In this paper, plants, specifications, and supervisors are modeled by Mealy automata, automata, and Moore automata, respectively. We define a composition of a supervisor and a plant coinductively, which is called a supervisory composition, to represent a behavior of the controlled plant. We formulate a supervisory control problem using the supervisory composition. We define two relations: a partial bisimulation relation and a modified normal relation. We show that these relations are related to the controllability/observability and the modified normality which are the key notions in the supervisory control theory.

## Keywords

discrete event systems supervisory control coalgebra

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## Authors and Affiliations

• Jun Kohjina
• 1
• Toshimitsu Ushio
• 1
• Yoshiki Kinoshita
• 2
1. 1.Graduate School of Engineering ScienceOsaka UniversityJapan
2. 2.National Institute of Advanced Industrial Science and TechnologyJapan