Optimal Stabilizing Controller for the Region of Weak Attraction under the Influence of Disturbances

Sasinee PRUEKPRASERT  Toshimitsu USHIO  

Publication
IEICE TRANSACTIONS on Information and Systems   Vol.E99-D   No.6   pp.1428-1435
Publication Date: 2016/06/01
Online ISSN: 1745-1361
DOI: 10.1587/transinf.2015FOP0004
Type of Manuscript: Special Section PAPER (Special Section on Formal Approach)
Category: Formal Methods
Keyword: 
stabilization,  state attraction,  quantitative discrete event systems,  state feedback controllers,  optimal control,  

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Summary: 
This paper considers an optimal stabilization problem of quantitative discrete event systems (DESs) under the influence of disturbances. We model a DES by a deterministic weighted automaton. The control cost is concerned with the sum of the weights along the generated trajectories reaching the target state. The region of weak attraction is the set of states of the system such that all trajectories starting from them can be controlled to reach a specified set of target states and stay there indefinitely. An optimal stabilizing controller is a controller that drives the states in this region to the set of target states with minimum control cost and keeps them there. We consider two control objectives: to minimize the worst-case control cost (1) subject to all enabled trajectories and (2) subject to the enabled trajectories starting by controllable events. Moreover, we consider the disturbances which are uncontrollable events that rarely occur in the real system but may degrade the control performance when they occur. We propose a linearithmic time algorithm for the synthesis of an optimal stabilizing controller which is robust to disturbances.