Nonlinear stochastic H2/H∞ control with multiple decision makers
Hiroaki Mukaidani · 2013
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.