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The Effects of Adding Input Redundancies in Linear Quadratic Regulator Problems

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Abstract

This paper investigates the effects of adding input redundancies repeatedly into linear quadratic regulator (LQR) problems. As the number of input redundancies increases, three equivalent conditions are stated to guarantee a strict decrease of the minimum cost, which is constrained by a pair of lower and upper bounds. The contribution of a new added input redundancy to reduce the minimum cost will diminish after more redundancies are added. Moreover, the minimum cost will converge to zero as the number of input redundancies goes toward infinity, which is proven by transferring the LQR problem into a cheap control problem.

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Authors and Affiliations

  1. State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing, 100871, China

    Zhongxing Peng, Ying Yang & Lin Huang

Authors
  1. Zhongxing Peng
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  2. Ying Yang
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  3. Lin Huang
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Corresponding author

Correspondence to Zhongxing Peng.

Additional information

Communicated by Felix L. Chernousko.

This work was supported by the National Natural Science Foundation of China under Grants 60874011, 90916003.

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Peng, Z., Yang, Y. & Huang, L. The Effects of Adding Input Redundancies in Linear Quadratic Regulator Problems. J Optim Theory Appl 150, 341–359 (2011). https://doi.org/10.1007/s10957-011-9845-z

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