Optimal Control of Multi-Stage Discrete Event Systems With Real-Time Constraints

Mao, Jianfeng; Cassandras, Christos G.

doi:10.1109/tac.2008.2009572

Cited by 22 publications

(15 citation statements)

References 17 publications

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“…The obvious next steps in this research are (1) to relax the homogeneity of the cost functions, in which case the zero queue property will no longer hold, and (2) to extend the VDA approach to m-stage systems (m > 2). Some preliminary results have been obtained in Mao and Cassandras (2006). Furthermore, as mentioned in Section II, our analysis has assumed that the optimization problem considered has feasible solutions.…”

Section: Discussionmentioning

confidence: 99%

Optimal Control of Two-Stage Discrete Event Systems with Real-Time Constraints

Mao

Cassandras

2007

Discrete Event Dyn Syst

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We consider discrete event systems (DES) involving tasks with real-time constraints and seek to control processing times so as to minimize a cost function subject to each task meeting its own constraint. When tasks are processed over a single stage, it has been shown that there are structural properties of the optimal sample path that lead to very efficient solutions of such problems. When tasks are processed over multiple stages and are subject to end-to-end real-time constraints, these properties no longer hold and no obvious extensions are known. We consider a two-stage problem with homogeneous cost functions over all tasks at each stage and derive several new optimality properties. These properties lead to the idea of introducing "virtual" deadlines at the first stage, thus partially decoupling the stages so that the known efficient solutions for single-stage problems can be used. We prove that the solution obtained by an iterative virtual deadline algorithm (VDA) converges to the global optimal solution of the two-stage problem and illustrate the efficiency of the VDA through numerical examples.

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Section: Discussionmentioning

confidence: 99%

Optimal Control of Two-Stage Discrete Event Systems with Real-Time Constraints

Mao

Cassandras

2007

Discrete Event Dyn Syst

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“…In such cases, the structural properties leading to the CTDA no longer apply. Nonetheless, it is possible to identify weaker structural properties that facilitate the derivation of efficient solution algorithms for two-stages (a tandem queueing system) , multiple stages in series (a serial line system) (Mao and Cassandras 2009b) and a multi-layer system (a layer-structured network) (Mao and Cassandras 2008) with end-to-end hard real-time constraints. The key idea is to assign "virtual deadlines" to each individual stage, thus partially decomposing the whole system into many singlestage systems where the efficiency of the CTDA can be fully utilized.…”

Section: Generalizationsmentioning

confidence: 99%

On-line Optimal Control of a Class of Discrete Event Systems with Real-Time Constraints

Mao

Cassandras

2009

Discrete Event Dyn Syst

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We consider Discrete Event Systems (DES) involving tasks with real-time constraints and seek to control processing times so as to minimize a cost function subject to each task meeting its own constraint. It has been shown that the off-line version of this problem can be efficiently solved by the Critical Task Decomposition Algorithm (CTDA) (Mao et al., IEEE Trans Mobile Comput 6(6): [678][679][680][681][682][683][684][685][686][687][688] 2007). In the on-line version, random task characteristics (e.g., arrival times) are not known in advance. To bypass this difficulty, worst-case analysis may be used. This, however, does not make use of probability distributions and results in an overly conservative solution. In this paper, we develop a new approach which does not rely on worst-case analysis but provides a "best solution in probability" efficiently obtained by estimating the probability distribution of sample-path-optimal solutions. We introduce a condition termed "non-singularity" under which the best solution in probability leads to the on-line optimal control. Numerical examples are included to illustrate our results and show substantial performance improvements over worstcase analysis.

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“…They propose a feedback controller for (max,+)-linear systems which delays input events as little as possible while constraints on internal or output events are satisfied. Authors of [21] and [22] consider discrete event systems involving tasks with real-time constraints and seek to control processing times so as to minimize a cost function subject to each task meeting its own constraint.…”

Section: Introductionmentioning

confidence: 99%

Feedback control for a class of discrete event systems with critical time

Amari

2015

International Journal of Control

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This paper presents an algebraic approach for control laws synthesis of timed event graphs subjected to strict temporal constraints. This class of discrete event systems is deterministic, in the sense that its behavior only depends on the initial marking and on the control that is applied. This behavior can be modeled by a linear equations system in Min-Plus algebra. The temporal constraint is represented by an inequality that is also linear in the Min-Plus algebra. Then, a method for the synthesis of control laws ensuring the respect of constraints is described. We give explicit formulas characterizing a control law, which ensures the validity of the temporal constraints. It is a causal feedback control, involving delays.The method is illustrated on an example.

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Optimal Control of Multi-Stage Discrete Event Systems With Real-Time Constraints

Cited by 22 publications

References 17 publications

Optimal Control of Two-Stage Discrete Event Systems with Real-Time Constraints

Optimal Control of Two-Stage Discrete Event Systems with Real-Time Constraints

On-line Optimal Control of a Class of Discrete Event Systems with Real-Time Constraints

Feedback control for a class of discrete event systems with critical time

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