Nonlinear stochastic H2/H∞ control with multiple decision makers

Author

Mukaidani, Hiroaki

Author_Institution

Inst. of Eng., Hiroshima Univ., Higashi-Hiroshima, Japan

fYear

2013

fDate

10-13 Dec. 2013

Firstpage

1186

Lastpage

1191

Abstract

In this paper, infinite-horizon H₂/H_∞ control problem for nonlinear stochastic system governed by Itô differential equation with multiple decision makers is investigated. A Nash game approach plays an important role in establishing a strategy set. After defining the equilibrium strategies, cross-coupled Hamilton-Jacobi-Bellman equations (HJBEs) are developed for the first time. In order to solve these equations, successive approximation is adapted to reduce the HJBE to a sequence of linear partial differential equations. In addition, Galerkin spectral method based on Chebyshev polynomials is combined. A simple numerical example are given to show the validity and potential of the proposed method.

Keywords

Chebyshev approximation; Galerkin method; H^∞ control; H² control; decision making; game theory; infinite horizon; nonlinear control systems; partial differential equations; polynomial approximation; stochastic systems; Chebyshev polynomials; Galerkin spectral method; HJBE; Itó differential equation; Nash game approach; cross-coupled Hamilton-Jacobi-Bellman equations; decision makers; infinite-horizon H₂-H_∞ control problem; linear partial differential equations; nonlinear stochastic H₂-H_∞ control; nonlinear stochastic system; Approximation algorithms; Chebyshev approximation; Equations; Games; Method of moments; Stochastic systems;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control (CDC), 2013 IEEE 52nd Annual Conference on

Conference_Location

Firenze

ISSN

0743-1546

Print_ISBN

978-1-4673-5714-2

Type

conf

DOI

10.1109/CDC.2013.6760043

Filename

6760043