Monte Carlo statistical prediction method for optimal control of linear hybrid systems

被引：0

作者：

State Key Laboratory of Industrial Control Technology, Institute of Industrial Process Control, Zhejiang University, Hangzhou 310027, China ^{[1
]}

机构：

[1] State Key Laboratory of Industrial Control Technology, Institute of Industrial Process Control, Zhejiang University

来源：

Zidonghua Xuebao | 2008年 / 8卷 / 1028-1032期

关键词：

Linear hybrid system; Monte Carlo statistical prediction (MCSP); Numerical solution; Optimal control;

D O I：

10.3724/SP.J.1004.2008.01028

中图分类号：

学科分类号：

摘要：

To reduce the computational complexity of optimal control of linear hybrid switching diffusion systems, a new Monte Carlo statistical prediction method is proposed. Firstly, the original optimal control problem in continuous time is approximated by a Markov decision problem in discrete time using numerical method; secondly, the numerical optimal control policies in some random sub-state spaces are obtained by reflecting boundary technique; and finally, the optimal control policy on the entire state space is predicted by statistical prediction based on the structure of the optimal control policy. The method can decrease the computational complexity and can be extended to cases of high dimension and large state space. Numerical examples illustrate and confirm the affectivity of the proposed method.

引用

页码：1028 / 1032

页数：4

共 11 条

[1]

Cassandras C.G., Lygeros J., Stochastic Hybrid Systems, (2007)

[2]

Zhang Q., Yin G.G., On nearly optimal controls of hybrid LQG problems, IEEE Transactions on Automatic Control, 44, 12, pp. 2271-2282, (1999)

[3]

Dragan V., Morozan T., The linear quadratic optimization problems for a class of linear stochastic systems with multiplicative white noise and Markovian jumping, IEEE Transactions on Automatic Control, 49, 5, pp. 665-675, (2004)

[4]

Boukas E.K., Haurie A., Manufacturing flow control and preventing maintenance: A stochastic control approach, IEEE Transactions on Automatic Control, 35, 9, pp. 1024-1031, (1990)

[5]

Yan H., Zhang Q., A numerical method in optimal production and setup scheduling of stochastic manufacturing systems, IEEE Transactions on Automatic Control, 42, 10, pp. 1452-1455, (1997)

[6]

Kushner H.J., Dupuis P.G., Numerical Methods for Stochastic Control Problems in Continuous Time (Second Edition), (2002)

[7]

Rishel R., Controlled Continuous Time Markov Process, (1990)

[8]

Sethi S.P., Zhang Q., Hierarchical Decision Making in Stochastic Manufacturing Systems, (1994)

[9]

Ghosh M.K., Arapostathis A., Marcus S.I., Optimal control of switching diffusions with application to flexible manufacturing systems, SIAM Journal on Control and Optimization, 31, 5, pp. 1183-1204, (1993)

[10]

Hyeong S.C., Fu M.C., Hu J.Q., Marcus S.I., Simulation-Based Algorithms for Markov Decision Processes, (2007)

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