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New solution bounds of the continuous algebraic Riccati equation and their applications in redundant control input systems

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Abstract

Redundant control inputs have wide applications in engineering, and have significant effects in quadratic performance optimal control, H2 control, tracking control, and many uncertain systems. In this paper, using some properties related to the inequality of the special matrix and the transformation of the matrix equation, we present new bounds of the solution of the continuous algebraic Riccati equation. The new bounds are more precise than those proposed in some existing studies on this topic. Subsequently, two lower bounds are presented for the optimal controller gain of the system (1), and a new upper bound is obtained for the optimal controller gain of the extended control system (3). Several examples are provided to demonstrate that our bounds of the optimal controller gain are superior to some previous results. Subsequently, we provide the applications of the new bounds in relevant redundant control problems and obtain good results. Finally, the corresponding numerical examples are provided to illustrate the effectiveness of our results and to compare them with the existing results.

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Acknowledgements

The work was supported in part by National Natural Science Foundation of China (Grant No. 11571292), National Natural Science Foundation for Youths of China (Grant No. 11801164), Key Project of National Natural Science Foundation of China (Grant No. 91430213), General Project of Hunan Provincial Natural Science Foundation (Grant No. 2015JJ2134), and General Project of Hunan Provincial Education Department of China (Grant No. 15C1320).

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Authors and Affiliations

  1. School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, China

    Jianzhou Liu & Li Wang

  2. School of Mathematics and Computational Science, Hunan University of Science and Technology, Xiangtan, 411201, China

    Li Wang

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  1. Jianzhou Liu
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  2. Li Wang
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Correspondence to Jianzhou Liu or Li Wang.

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Liu, J., Wang, L. New solution bounds of the continuous algebraic Riccati equation and their applications in redundant control input systems. Sci. China Inf. Sci. 62, 202201 (2019). https://doi.org/10.1007/s11432-017-9553-5

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  • DOI: https://doi.org/10.1007/s11432-017-9553-5

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