Title :
Nonlinear stochastic H2/H∞ control with multiple decision makers
Author :
Mukaidani, Hiroaki
Author_Institution :
Inst. of Eng., Hiroshima Univ., Higashi-Hiroshima, Japan
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;
Conference_Titel :
Decision and Control (CDC), 2013 IEEE 52nd Annual Conference on
Conference_Location :
Firenze
Print_ISBN :
978-1-4673-5714-2
DOI :
10.1109/CDC.2013.6760043
