This is the first work in its type trying to optimize the set of controls for a state feedback. Controlled Dan/Petri nets + is a modeling framework based on Place/Transitions Nets used to model a control-logic called multiple and simultaneous control (MSC) which can reduce the size of the set of controls. In this paper we present the subnet structure called Σ f(q) to model the MSC-logic and an algorithm to design an optimal state feedback with a set of controls for a class of Dan/Petri Net + having a single-place connected circuits and the conditions to obtain a maximally permissive and optimal state feedback.
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 + (Ctrl D/PN + ); 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 + and present the net structure Σ n a(q)-y to model the MSC-logic.
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