Enforcing the optimal set of controls for state feedback with non-redundant controllers

Abstract

Optimal control sets are defined as sets with a smaller cardinality than the cardinality of the set of controlled transitions and obtained when modeling control systems with a multiple and simultaneous control (MSC) approach using Controlled Dan/Petri nets <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> (Ctrl D/PN <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> ); optimal and non-redundant control sets are defined as optimal sets without controllers that result redundantly in terms of a set of admissible markings with specific characteristics. In this paper we explain how to find the optimal an non-redundant set of controls in control systems modeled with Ctrl D/PN <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> and present the net structure ∑ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</inf> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a(q)−y</sup> to model the MSC-logic.