Control Of Timed Event Graphs Research Articles

Optimal output feedback control of Timed Event Graphs including disturbances in a resource sharing environment

Timed event graphs (TEGs) constitute a subclass of timed Petri nets that model synchronization and delay phenomena, but not conflict or choice. In a suitable mathematical framework (idempotent semirings such as the min-plus algebra), the temporal evolution of TEGs can be described by a set of linear equations. Recently, a method has been proposed for the optimal feedforward control of systems of TEGs that share one or more resources based on a prespecified priority policy. In this paper, we propose a feedback solution to deal with disturbances in such systems, which is not possible under the current feedforward approaches.

A Novel Approach to the Modeling and Control of Timed Event Graphs with Partial Synchronization

Timed event graphs (TEGs) are a subclass of timed Petri nets whose dynamics is governed by standard synchronization, i. e., a transition is enabled to fire a certain time after the firing of some other transition(s) and is never disabled by the firing of other transitions. Partial synchronization (PS) imposes an additional condition: a partially synchronized transition can only fire within certain time windows determined by an external signal. Considering TEGs with PS allows to express time-varying behavior, which is manifested in several scenarios of practical relevance. We propose an original approach to model and control TEGs with PS, developed entirely within the domain of the dioid of counters, on which a well-consolidated control theory is available. Additionally, we show that our method can be combined with recent results and applied to the optimal control of TEGs with both PS and resource-sharing phenomena.

Optimal Control of Timed Event Graphs with Resource Sharing and Output-Reference Update

Abstract Discrete-event systems exhibiting synchronization and delay phenomena, but not conflict, can be modeled as timed event graphs (TEGs), which admit a linear representation in some idempotent semirings. For such linear systems, a control theory has been constructed. In this paper, we build onto this control framework by proposing a formal method to determine the optimal (just-in-time) control inputs in face of changes in the output-references for a number of TEGs that share one or more resources. The approach is based on a prespecified priority policy among the component subsystems. Simple examples are presented to illustrate the results.

State‐Feedback Control for a Class of Timed Petri Nets Subject to Marking Constraints

AbstractThe paper contributes with an original method of designing a control for discrete event systems modeled by a class of timed Petri nets. Precisely, this work deals with the closed loop control of Timed Event Graphs (TEGs) under specifications expressed with linear marking constraints. The objective of the controller is to limit the number of tokens in some places of these TEGs. The behavior of TEGs is represented by a system of difference equations that are linear in Min‐Plus algebra and the constraints are described by a set of inequalities, which are also linear in Min‐Plus algebra. A formal approach to design control laws that guarantee compliance with these marking constraints is proposed. For this, two sufficient conditions for the existence of control laws are proposed. The computed controls are causal feedbacks, which can be represented by a set of marked and timed places. The proposed method is illustrated in two applications: a manufacturing production line and an assembly system.

On the Steady-State Control of Timed Event Graphs With Firing Date Constraints

Two algorithms for solving a specific class of steady-state control problems for Timed Event Graphs are presented. In the first, asymptotic convergence to the desired set is guaranteed. The second algorithm, which builds on from the recent developments in the spectral theory of min-max functions, guarantees Lyapunov stability since the distance between the actual state and the desired set never increases. Simulation results show the efficiency of the proposed approach in a problem of moderate complexity.

Compromise approach for predictive control of Timed Event Graphs with specifications defined by P-time Event Graphs

In this paper, the aim is to make the predictive control of a plant described by a Timed Event Graph which follows the specifications defined by a P-time Event Graph. We propose a compromise approach between the ideal optimality of the solution and the on-line application of the computed solution when the relevant optimal control cannot be applied for a given computer. The technique is based on a reduction of the number of iterations of the fixed point algorithm such that the computed control remains causal. The analysis of the partial satisfaction of the specifications at each iteration of the algorithm defined in the (max, + ) algebra shows that a subset of constraints is guaranteed by the control computed at each iteration while another one is possibly satisfied.

Causality phenomenon and Compromise Technique for Predictive Control of Timed Event Graphs with Specifications Defined by P-time Event Graphs

An imperative condition of operation in Predictive Control is that a control must be applied after the end of its calculation. In this paper, we analyze and formalize this causality phenomenon which depends on both the computer time and the control problem. Two techniques are proposed. When the causality forbids the complete convergence of the algorithm, we propose a compromise technique which needs the analysis of the partial satisfaction of the specifications at each iteration of the algorithm. The plant is described by a Timed Event Graph while the specifications are defined by a P-time Event Graph.

Predictive control of Timed Event Graphs with specifications defined by P-time Event Graphs

The aim of this paper is the predictive control of Timed Event Graphs with specifications defined by P-time Event Graphs. We propose a fixed-point approach which leads to a pseudo-polynomial algorithm. As the performance of the algorithm is crucial in on-line control, we highlight an important case where the resolution of this first algorithm is efficient. The second technique is a space controller on a horizon leading to a strongly polynomial algorithm.