Control of (max,+) automata: Logical and timing aspects

A new framework for control of (max,+) automata is introduced. The tensor product of their linear representations used in this paper is an extension of parallel composition from Boolean to (max,+) automata and can be nicely applied to both logical and timing aspects of supervisory control. Case of uncontrollable events that can neither be disabled nor delayed is studied within a behavioral framework. Optimal (least restrictive) control of (max,+) automata is studied using residuation theory applied to Hadamard product of (multivariable) formal power series.