Optimal Linear Quadratic Regulator of Switched Systems

Guangyu Wu; Jian Sun; Jie Chen

doi:10.1109/TAC.2018.2872204

Optimal Linear Quadratic Regulator of Switched Systems

Guangyu Wu, Jian Sun^*, Jie Chen

^*Corresponding author for this work

School of Automation

Beijing Institute of Technology

Research output: Contribution to journal › Article › peer-review

73 Citations (Scopus)

Abstract

This paper considers the optimal control problem of linear switched systems with linear quadratic (LQ) cost or multiple LQ cost. By adopting an embedding transformation, the switching design problem is relaxed and transformed into a traditional optimal control problem. The bang-bang-Type solutions of the embedded optimal control problems are obtained for both the positive definite LQ cost case and the multiple LQ cost case, which are the optimal solutions to the original problems. The switching sequence of modes and the switching instants can be calculated by solving a closed-form optimal switching condition. The optimal state feedback control law is determined simultaneously. Finally, numerical results are provided to illustrate the effectiveness of the proposed method.

Original language	English
Article number	8472172
Pages (from-to)	2898-2904
Number of pages	7
Journal	IEEE Transactions on Automatic Control
Volume	64
Issue number	7
DOIs	https://doi.org/10.1109/TAC.2018.2872204
Publication status	Published - Jul 2019

Keywords

Bang-bang-Type solution
optimal control
quadratic programming
switched system
switching condition

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10.1109/TAC.2018.2872204

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Wu, G., Sun, J., & Chen, J. (2019). Optimal Linear Quadratic Regulator of Switched Systems. IEEE Transactions on Automatic Control, 64(7), 2898-2904. Article 8472172. https://doi.org/10.1109/TAC.2018.2872204

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abstract = "This paper considers the optimal control problem of linear switched systems with linear quadratic (LQ) cost or multiple LQ cost. By adopting an embedding transformation, the switching design problem is relaxed and transformed into a traditional optimal control problem. The bang-bang-Type solutions of the embedded optimal control problems are obtained for both the positive definite LQ cost case and the multiple LQ cost case, which are the optimal solutions to the original problems. The switching sequence of modes and the switching instants can be calculated by solving a closed-form optimal switching condition. The optimal state feedback control law is determined simultaneously. Finally, numerical results are provided to illustrate the effectiveness of the proposed method.",

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AB - This paper considers the optimal control problem of linear switched systems with linear quadratic (LQ) cost or multiple LQ cost. By adopting an embedding transformation, the switching design problem is relaxed and transformed into a traditional optimal control problem. The bang-bang-Type solutions of the embedded optimal control problems are obtained for both the positive definite LQ cost case and the multiple LQ cost case, which are the optimal solutions to the original problems. The switching sequence of modes and the switching instants can be calculated by solving a closed-form optimal switching condition. The optimal state feedback control law is determined simultaneously. Finally, numerical results are provided to illustrate the effectiveness of the proposed method.

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KW - quadratic programming

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Optimal Linear Quadratic Regulator of Switched Systems

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