American Institute of Mathematical Sciences

Advanced
January  2006, 2(1): 63-80. doi: 10.3934/jimo.2006.2.63

Optimal control for resource allocation in discrete event systems

Qiying Hu 1, and  Wuyi Yue 2,

1. 

College of International Business and Management, Shanghai University, Shanghai 201800, China
2. 

Department of Intelligence and Informatics, Konan University, 8-9-1 Okamoto, Kobe 658-8501

Received  August 2005 Revised  November 2005 Published  January 2006

Supervisory control for discrete event systems (DESs) belongs essentially to the logic level for control problems in DESs. Its corresponding control task is hard. In this paper, we study a new optimal control problem in DESs. The performance measure is to maximize the maximal discounted total reward among all possible strings (i.e., paths) of the controlled system. The condition we need for this is only that the performance measure is well defined. We then divide the problem into three sub-cases where the optimal values are respectively finite, positive infinite and negative infinite. We then show the optimality equation in the case with a finite optimal value. Also, we characterize the optimality equation together with its solutions and characterize the structure of the set of all optimal policies. All the results are still true when the performance measure is to maximize the minimal discounted total reward among all possible strings of the controlled system. Finally, we apply these equations and solutions to a resource allocation system. The system may be deadlocked and in order to avoid the deadlock we can either prohibit occurrence of some events or resolve the deadlock. It is shown that from the view of the maximal discounted total cost, it is better to resolve the deadlock if and only if the cost for resolving the deadlock is less than the threshold value.
Keywords: resource allocation system., discrete event systems, Optimal control.
Mathematics Subject Classification: 37V45, 90C4.
Citation: Qiying Hu, Wuyi Yue. Optimal control for resource allocation in discrete event systems. Journal of Industrial & Management Optimization, 2006, 2 (1) : 63-80. doi: 10.3934/jimo.2006.2.63
[1]

Qiying Hu, Wuyi Yue. Optimal control for discrete event systems with arbitrary control pattern. Discrete & Continuous Dynamical Systems - B, 2006, 6 (3) : 535-558. doi: 10.3934/dcdsb.2006.6.535
[2]

Qiying Hu, Wuyi Yue. Two new optimal models for controlling discrete event systems. Journal of Industrial & Management Optimization, 2005, 1 (1) : 65-80. doi: 10.3934/jimo.2005.1.65
[3]

Semu Mitiku Kassa. Three-level global resource allocation model for HIV control: A hierarchical decision system approach. Mathematical Biosciences & Engineering, 2018, 15 (1) : 255-273. doi: 10.3934/mbe.2018011
[4]

Alexei Korolev, Gennady Ougolnitsky. Optimal resource allocation in the difference and differential Stackelberg games on marketing networks. Journal of Dynamics & Games, 2020, 7 (2) : 141-162. doi: 10.3934/jdg.2020009
[5]

Ali Gharouni, Lin Wang. Modeling the spread of bed bug infestation and optimal resource allocation for disinfestation. Mathematical Biosciences & Engineering, 2016, 13 (5) : 969-980. doi: 10.3934/mbe.2016025
[6]

Qiying Hu, Chen Xu, Wuyi Yue. A unified model for state feedback of discrete event systems II: Control synthesis problems. Journal of Industrial & Management Optimization, 2008, 4 (4) : 713-726. doi: 10.3934/jimo.2008.4.713
[7]

Yuan Xu, Xin Jin, Saiwei Wang, Yang Tang. Optimal synchronization control of multiple euler-lagrange systems via event-triggered reinforcement learning. Discrete & Continuous Dynamical Systems - S, 2021, 14 (4) : 1495-1518. doi: 10.3934/dcdss.2020377
[8]

Sang-Heon Lee. Development of concurrent structural decentralised discrete event system using bisimulation concept. Numerical Algebra, Control & Optimization, 2016, 6 (3) : 305-317. doi: 10.3934/naco.2016013
[9]

Galina Kurina, Sahlar Meherrem. Decomposition of discrete linear-quadratic optimal control problems for switching systems. Conference Publications, 2015, 2015 (special) : 764-774. doi: 10.3934/proc.2015.0764
[10]

Peng Cheng, Yanqing Liu, Yanyan Yin, Song Wang, Feng Pan. Fuzzy event-triggered disturbance rejection control of nonlinear systems. Journal of Industrial & Management Optimization, 2021, 17 (6) : 3297-3307. doi: 10.3934/jimo.2020119
[11]

Stefan Jerg, Oliver Junge, Marcus Post. Global optimal feedbacks for stochastic quantized nonlinear event systems. Journal of Computational Dynamics, 2014, 1 (1) : 163-176. doi: 10.3934/jcd.2014.1.163
[12]

Anthony M. Bloch, Peter E. Crouch, Nikolaj Nordkvist. Continuous and discrete embedded optimal control problems and their application to the analysis of Clebsch optimal control problems and mechanical systems. Journal of Geometric Mechanics, 2013, 5 (1) : 1-38. doi: 10.3934/jgm.2013.5.1
[13]

Sedighe Asghariniya, Hamed Zhiani Rezai, Saeid Mehrabian. Resource allocation: A common set of weights model. Numerical Algebra, Control & Optimization, 2020, 10 (3) : 257-273. doi: 10.3934/naco.2020001
[14]

Irina Kareva, Faina Berezovkaya, Georgy Karev. Mixed strategies and natural selection in resource allocation. Mathematical Biosciences & Engineering, 2013, 10 (5&6) : 1561-1586. doi: 10.3934/mbe.2013.10.1561
[15]

Qinglan Xia, Shaofeng Xu. On the ramified optimal allocation problem. Networks & Heterogeneous Media, 2013, 8 (2) : 591-624. doi: 10.3934/nhm.2013.8.591
[16]

Qiying Hu, Chen Xu, Wuyi Yue. A unified model for state feedback of discrete event systems I: framework and maximal permissive state feedback. Journal of Industrial & Management Optimization, 2008, 4 (1) : 107-123. doi: 10.3934/jimo.2008.4.107
[17]

Yadong Shu, Bo Li. Linear-quadratic optimal control for discrete-time stochastic descriptor systems. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021034
[18]

Yuefen Chen, Yuanguo Zhu. Indefinite LQ optimal control with process state inequality constraints for discrete-time uncertain systems. Journal of Industrial & Management Optimization, 2018, 14 (3) : 913-930. doi: 10.3934/jimo.2017082
[19]

Masashi Wakaiki, Hideki Sano. Stability analysis of infinite-dimensional event-triggered and self-triggered control systems with Lipschitz perturbations. Mathematical Control & Related Fields, 2021  doi: 10.3934/mcrf.2021021
[20]

Hongru Ren, Shubo Li, Changxin Lu. Event-triggered adaptive fault-tolerant control for multi-agent systems with unknown disturbances. Discrete & Continuous Dynamical Systems - S, 2021, 14 (4) : 1395-1414. doi: 10.3934/dcdss.2020379

2020 Impact Factor: 1.801

Tools

Metrics

  • PDF downloads (45)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences