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Robust Optimal Control of Continuous Linear Quadratic System Subject to Disturbances

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Optimization and Control Methods in Industrial Engineering and Construction

Part of the book series: Intelligent Systems, Control and Automation: Science and Engineering ((ISCA,volume 72))

Abstract

In this chapter, the robust optimal control of linear quadratic system is considered. This problem is first formulated as a minimax optimal control problem. We prove that it admits a solution. Based on this result, we show that this infinite-dimensional minimax optimal control problem can be approximated by a sequence of finite-dimensional minimax optimal parameter selection problems. Furthermore, these finite-dimensional minimax optimal parameter selection problems can be transformed into semi-definite programming problems or standard minimization problems. A numerical example is presented to illustrate the developed method.

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Acknowledgments

Changzhi Wu was partially supported by NSFC 11001288, the key project of Chinese Ministry of Education 210179, and the project from Chongqing Nature Science Foundation cstc2013jjB0149 and cstc2013jcyjA1338.

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Authors and Affiliations

  1. School of Built Environment, Curtin University, Perth, WA, 6845, Australia

    Changzhi Wu & Xiangyu Wang

  2. School of Mathematics and Statistics, Curtin University, Perth, WA, 6845, Australia

    Kok Lay Teo

  3. School of Mathematics, Anhui Normal University, 241000, Wuhu, China

    Lin Jiang

Authors
  1. Changzhi Wu
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  2. Xiangyu Wang
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  3. Kok Lay Teo
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  4. Lin Jiang
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Corresponding author

Correspondence to Changzhi Wu .

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Editors and Affiliations

  1. Dept of Mathematics & Statistics, Curtin University, Perth, West Australia, Australia

    Honglei Xu

  2. School of Built Environment, Curtin University, Perth, West Australia, Australia

    Xiangyu Wang

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Wu, C., Wang, X., Teo, K.L., Jiang, L. (2014). Robust Optimal Control of Continuous Linear Quadratic System Subject to Disturbances. In: Xu, H., Wang, X. (eds) Optimization and Control Methods in Industrial Engineering and Construction. Intelligent Systems, Control and Automation: Science and Engineering, vol 72. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-8044-5_2

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  • DOI: https://doi.org/10.1007/978-94-017-8044-5_2

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  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-017-8043-8

  • Online ISBN: 978-94-017-8044-5

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