Real-world applications, including supply chains, flexible industrial systems, networked control, and urban transport, frequently exhibit the structure of Discrete Event Systems (DES). This study focuses on controlling DES subject to disturbances while ensuring strict time constraints, specifically addressing partially controllable and observable timed event graphs. The behavior of these graphs is modeled using Min-Plus algebra and linear inequalities, which are then used to formalize the constraints to be satisfied. An algebraic approach for designing control laws to meet these restrictions is proposed. Sufficient conditions for the existence of causal state feedback that guarantees specification satisfaction are established. The approach is validated through a disturbed supply chain application, where controllers are implemented as timed and marked places, acting as supervisors to prevent constraint violations.

This paper addresses the control problem related to marking and strict timing constraints in Timed Event Graphs (TEGs). An analytic approach is developed to design state feedback control laws using Min-Plus formalism. In this approach, the dynamic behavior of TEGs and the mixed constraints are represented by linear equations and inequalities within the Min-Plus algebra dioid. Utilizing these mathematical frameworks, control laws are formulated to enforce the required constraints on TEG paths, provided certain sufficient conditions are met. The proposed controllers are implemented through a set of monitor places that oversee the initial TEGs, ensuring all mixed constraints are satisfied. Finally, a manufacturing system case study is presented to demonstrate the theoretical results and validate the effectiveness of the proposed methods.

International audience

This paper provides an algebraic control strategy for solving the problem of generalized mutual exclusion constraints in a network of timed event graphs with disturbance transitions. To this end, linear Min-Plus equations are used to describe the behavior of this class of timed Petri nets, and weighted Min-Plus inequalities translate the constraints to be satisfied. By combining these mathematical formalisms, sufficient conditions for the existence of control laws guaranteeing these mutual exclusion constraints are proposed. The theoretical results presented in this study are applied to accommodate supply disruptions from two suppliers to reconfigured manufacturing line.