Abstract
This paper is concerned with the algorithms which solveH2/H∞control problems of stochastic systems with state-dependent noise. Firstly, the algorithms for the finite and infinite horizonH2/H∞control of discrete-time stochastic systems are reviewed and studied. Secondly, two algorithms are proposed for the finite and infinite horizonH2/H∞control of continuous-time stochastic systems, respectively. Finally, several numerical examples are presented to show the effectiveness of the algorithms.
Highlights
Mixed H2/H∞ control is an important robust control method and has been extensively investigated by many researchers [1,2,3,4]
The algorithm for stochastic H2/H∞ control of continuous-time systems has received little research attention. This is because the coupled matrix-valued equations for the continuoustime H2/H∞ control cannot be solved by recursive algorithms as in the discrete-time case
For continuous-time stochastic systems, two algorithms are Mathematical Problems in Engineering proposed for the finite and infinite horizon H2/H∞ control, respectively
Summary
Mixed H2/H∞ control is an important robust control method and has been extensively investigated by many researchers [1,2,3,4]. The finite and infinite horizon H2/H∞ control problems were solved for discrete-time stochastic systems with state and disturbance dependent noise by [6] and [7], respectively. In [15], an iterative algorithm was proposed to solve a kind of stochastic algebraic Riccati equation in LQ zero-sum game problems Most of these algorithms were concerned with the H2/H∞ control for discrete-time systems. The algorithm for stochastic H2/H∞ control of continuous-time systems has received little research attention This is because the coupled matrix-valued equations for the continuoustime H2/H∞ control cannot be solved by recursive algorithms as in the discrete-time case. For continuous-time stochastic systems, two algorithms are Mathematical Problems in Engineering proposed for the finite and infinite horizon H2/H∞ control, respectively. We make use of the following notations throughout this paper: Rn: n-dimensional Euclidean space; Sn: the set of all n×n symmetric matrices; A > 0 (A ≥ 0): A is a positive definite (positive semidefinite) symmetric matrix; A: the transpose of a matrix A; I: the identity matrix; Tr[A]: the trace of matrix A; E(x): the mathematical expectation of x
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