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Composite Stackelberg Strategy for Singularly Perturbed Bilinear Quadratic Systems

Author

Listed:
  • Bin Ning

    (School of Management, Guangdong University of Technology, Guangzhou, 510520, China)

  • Zhang Chengke

    (School of Commerce & Economics, Guangdong University of Technology, Guangzhou, 510520, China)

  • Zhu Huainian

    (School of Management, Guangdong University of Technology, Guangzhou, 510520, China)

  • Mo Zan

    (School of Management, Guangdong University of Technology, Guangzhou, 510520, China)

Abstract

Based on singularly perturbed bilinear quadratic problems, this paper proposes to decompose the full-order system into two subsystems of a slow-time and fast-time scale. Utilizing the fixed point iterative algorithm to solve cross-coupled algebraic Riccati equations, equilibrium strategies of the two subsystems can be obtained, and further the composite strategy of the original full-order system. It was proved that such a composite strategy formed an o(ε) (near) Stackelberg equilibrium, and a numerical result of the algorithm was presented in the end.

Suggested Citation

  • Bin Ning & Zhang Chengke & Zhu Huainian & Mo Zan, 2015. "Composite Stackelberg Strategy for Singularly Perturbed Bilinear Quadratic Systems," Journal of Systems Science and Information, De Gruyter, vol. 3(2), pages 154-163, April.
    • Handle: RePEc:bpj:jossai:v:3:y:2015:i:2:p:154-163:n:5
    DOI: 10.1515/JSSI-2015-0154
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    References listed on IDEAS

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    1. Chander, Parkash, 1983. "The nonlinear input-output model," Journal of Economic Theory, Elsevier, vol. 30(2), pages 219-229, August.
    2. William M. McEneaney, 1997. "A Robust Control Framework for Option Pricing," Mathematics of Operations Research, INFORMS, vol. 22(1), pages 202-221, February.
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