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Pareto Efficiency of Finite Horizon Switched Linear Quadratic Differential Games

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Abstract

A switched linear quadratic (LQ) differential game over finite-horizon is investigated in this paper. The switching signal is regarded as a non-conventional player, afterwards the definition of Pareto efficiency is extended to dynamics switching situations to characterize the solutions of this multi-objective problem. Furthermore, the switched differential game is equivalently transformed into a family of parameterized single-objective optimal problems by introducing preference information and auxiliary variables. This transformation reduces the computing complexity such that the Pareto frontier of the switched LQ differential game can be constructed by dynamic programming. Finally, a numerical example is provided to illustrate the effectiveness.

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Authors and Affiliations

  1. College of Information Science and Engineering, Northeastern University, Shenyang, 110819, China

    Yabing Huang & Jun Zhao

  2. State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, 110819, China

    Yabing Huang & Jun Zhao

Authors
  1. Yabing Huang
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  2. Jun Zhao
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Corresponding author

Correspondence to Jun Zhao.

Additional information

This work was supported by the National Natural Science Foundation of China under Grant No. 61773098 and the 111 Project under Grant No. B16009.

This paper was recommended for publication by Guest Editor LIU Tengfei.

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Huang, Y., Zhao, J. Pareto Efficiency of Finite Horizon Switched Linear Quadratic Differential Games. J Syst Sci Complex 31, 173–187 (2018). https://doi.org/10.1007/s11424-018-7439-7

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  • DOI: https://doi.org/10.1007/s11424-018-7439-7

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