Control Problem in Max Plus Linear Model with Temporal Constraints

• Published in: Revista iberoamericana de automática e informática industrial Vol. 13; no. 4; pp. 438 - 449
• Main Authors: C. Cárdenas, J. Cardillo, J.J. Loiseau, C. Martínez
• Format: Journal Article
• Language: Spanish
• Published: Universitat Politècnica de València 01.10.2016
• Subjects: Algebra Max Plus; Grafos de Eventos Temporizados (GETs); Restricciones Temporales; Sistemas de Eventos Discretos (SED)
• ISSN: 1697-7912; 1697-7920
• DOI: 10.1016/j.riai.2016.07.001

This article deals with the control of discrete event systems subject to synchronization and delay phenomena, described by a plus max linear model. The temporal constraints are imposed on the state space of the system. These constraints are described in the max plus cone defined by the image of the Kleene star of the matrix associated with the temporal constraints. In consequence, the problem of determining a control that force the satisfaction of time constraints, is formulated in terms of the invariance of the cone. Sufficient conditions for the existence of a solution to this problem have been established. Our approach allows the design of a satisfactory control of the form of a static state feedback. We emphasize that our solution takes into account two aspects which are the initialization of the control law, and its causality, important for its implementation. To illustrate the application of this approach, two control problems are presented.