Composite Stackelberg Strategy for Singularly Perturbed Bilinear Quadratic Systems

Bin Ning (), Zhang Chengke (), Zhu Huainian () and Mo Zan ()
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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

Journal of Systems Science and Information, 2015, vol. 3, issue 2, 154-163

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.

Keywords: singularly perturbed; bilinear quadratic system; stackelberg equilibrium (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:bpj:jossai:v:3:y:2015:i:2:p:154-163:n:5

DOI: 10.1515/JSSI-2015-0154

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