Synthesis of Inference-Based Decentralized Control for Discrete Event Systems

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In our past work, we presented a framework for the decentralized control of discrete event systems involving inferencing over ambiguities, about the system state, of various local decision makers. Using the knowledge of the self-ambiguity and those of the others, each local control decision is tagged with a certain ambiguity level (level zero being the minimum and representing no ambiguity). A global control decision is taken to be a “winning'' local control decision, i.e., one with a minimum ambiguity level. For the existence of a decentralized supervisor, so that for each controllable event the ambiguity levels of all winning disablement or enablement decisions are bounded by some number <formula formulatype="inline"><tex>$N$</tex></formula> (such a supervisor is termed <formula formulatype="inline"><tex>$N$</tex></formula>-inferring), the notion of <formula formulatype="inline"><tex>$N$</tex></formula>-inference-observability was introduced. When the given specification fails to satisfy the <formula formulatype="inline"><tex>$N$</tex></formula>-inference-observability property, an <formula formulatype="inline"><tex>$N$</tex></formula>-inferring supervisor achieving the entire specification does not exist. We first show that the class of <formula formulatype="inline"><tex>$N$</tex></formula>-inference-observable sublanguages is not closed under union implying that the supremal <formula formulatype="inline"><tex>$N$</tex></formula>-inference-observable sublanguage need not exist. We next provide a technique for synthesizing an <formula formulatype="inline"><tex>$N$</tex></formula>-inferring decentralized supervisor that achieves an <formula formulatype="inline"><tex>$N$</tex></formula>-inference-observable <emphasis emphasistype="italic">sublanguage </emphasis> of the specification. The sublanguage achieved equals the specification language when the specification itself is <formula formulatype="inline"><tex>$N$</tex></formula>-inference-observable. A </para>