Modal Logics for Timed Control

In this paper we use the timed modal logic MediaObjects/InlineFigure1.png to specify control objectives for timed plants. We show that the control problem for a large class of objectives can be reduced to a model-checking problem for an extension ( MediaObjects/InlineFigure2.png) of the logic MediaObjects/InlineFigure3.png with a new modality. More precisely we define a fragment of MediaObjects/InlineFigure4.png, namely MediaObjects/InlineFigure5.png, such that any control objective of MediaObjects/InlineFigure6.png, can be translated into a MediaObjects/InlineFigure7.png, formula that holds for the plant if and only if there is a controller that can enforce the control objective. We also show that the new modality of MediaObjects/InlineFigure8.png, strictly increases the expressive power of MediaObjects/InlineFigure9.png, while model-checking of MediaObjects/InlineFigure10.png, remains EXPTIME-complete. Work supported by ACI Cortos, a program of the French government.

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