Online Sensor Activation for Detectability of Discrete Event Systems

In this paper, we investigate online sensor activation to ensure detectability of discrete event systems. Detectability requires that states of a system can be determined or certain pairs of states can be distinguished by an external observer eventually or periodically. Since minimal sensor activation policies for detectability may not exist, two new concepts are introduced: 1) <formula formulatype="inline"><tex Notation="TeX">$k$</tex></formula>-step distinguishability is introduced for strong detectability and 2) information-preserving is introduced for strong periodic detectability. The online sensor activation is then proposed and is based on the best state estimate available at the time of decision making. Three algorithms are developed for online sensor activation. The first two algorithms are for strong detectability. They minimize sensor activation while preserving <formula formulatype="inline"><tex Notation="TeX">$k$</tex> </formula>-step distinguishability. The third algorithm deals with strong periodic detectability. It minimizes sensor activation while preserving state information.

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