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.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Bertsekas DP (1999) Nonlinear programming (2nd edn). Athena Scientific, Belmont, MA
Cassandras CG, Liu Q, Gokbayrak K, Pepyne DL (1999) Optimal control of a two-stage hybrid manufacturing system model. In: Proceedings of the 38th IEEE Conference on Decision and Control, pp 450–455, Dec.
Cassandras CG, Pepyne DL, Wardi Y (2001) Optimal control of a class of hybrid system. IEEE Trans Automat Contr 46(3):398–415
Cho YC, Cassandras CG, Pepyne DL (2001) Forward decomposition algorithms for optimal control of a class of hybrid systems. Int J Robust Nonlinear Control 11(5):497–513
Gokbayrak K, Cassandras CG (2000) Constrained optimal control for multistage hybrid manufacturing system models. In: Proceedings of 8th IEEE Mediterranean Conference on New Directions in Control and Automation, July 2000
Liu JWS (2000) Real-time system. Prentice-Hall
Mao J, Cassandras CG (2006) Optimal control of multi-stage discrete event systems with real-time constraints. In: Proc. of 45rd IEEE Conf. Decision and Control, pp 1057–1062, Dec.
Mao J, Cassandras CG (2007) Optimal admission control of discrete event systems with real-time constraints. Submitted to Proc. of 46rd IEEE Conf. Decision and Control
Mao JF, Cassandras CG, Zhao QC (2004) Optimal dynamic voltage scaling in power-limited systems with real-time constraints. Decis Contr 2(14–17):1472–1477
Mao J, Zhao Q, Cassandras CG (2004) Optimal dynamic voltage scaling in power-limited systems with real-time constraints. In: Proc. of 43rd IEEE Conf. Decision and Control, pp 1472–1477, Dec.
Miao L, Cassandras CG (2006) Optimal transmission scheduling for energy-efficient wireless networks. In: Proceedings of INFOCOM
Miao L, Cassandras CG (2007) Receding horizon control for a class of discrete event systems with real-time constraints. IEEE Trans Automat Contr 52(5):825–839
Pepyne DL, Cassandras CG (2000) Optimal control of hybrid systems in manufacturing. In: Proceedings of the IEEE, vol. 88, pp 1108–1123
The authors’ work is supported in part by the National Science Foundation under Grant DMI-0330171, by AFOSR under grants FA9550-04-1-0133 and FA9550-04-1-0208, by DOE under grant DE-FG52-06NA27490, and by ARO under grant DAAD19-01-0610.
About this article
Cite this article
Mao, J., Cassandras, C.G. Optimal Control of Two-Stage Discrete Event Systems with Real-Time Constraints. Discrete Event Dyn Syst 17, 505–529 (2007). https://doi.org/10.1007/s10626-007-0019-y
- Discrete event system
- Optimal control
- Real-time constraint