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The effects of redundant control inputs in optimal control

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Abstract

For a stabilizable system, the extension of the control inputs has no use for stabilizability, but it is important for optimal control. In this paper, a necessary and sufficient condition is presented to strictly decrease the quadratic optimal performance index after control input extensions. A similar result is also provided for H 2 optimal control problem. These results show an essential difference between single-input and multi-input control systems. Several examples are taken to illustrate related problems.

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Authors and Affiliations

  1. State Key Lab for Turbulence and Complex Systems and Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing, 100871, China

    ZhiSheng Duan, Lin Huang & Ying Yang

Authors
  1. ZhiSheng Duan
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  2. Lin Huang
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  3. Ying Yang
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Corresponding author

Correspondence to ZhiSheng Duan.

Additional information

Supported by the National Natural Science Foundation of China (Grant Nos. 90916003, 60674093, 60874011), and the Key Projects of Educational Ministry of China (Grant No. 107110)

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Duan, Z., Huang, L. & Yang, Y. The effects of redundant control inputs in optimal control. Sci. China Ser. F-Inf. Sci. 52, 1973–1981 (2009). https://doi.org/10.1007/s11432-009-0189-3

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  • DOI: https://doi.org/10.1007/s11432-009-0189-3

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