A MAXIMUM PRINCIPLE APPROACH TO STOCHASTIC H2/H∞ CONTROL WITH RANDOM JUMPS

doi:10.1016/S0252-9602(15)60006-6

数学物理学报(英文版) ›› 2015, Vol. 35 ›› Issue (2): 348-358.doi: 10.1016/S0252-9602(15)60006-6

A MAXIMUM PRINCIPLE APPROACH TO STOCHASTIC H₂/H_∞ CONTROL WITH RANDOM JUMPS

张启侠¹, 孙启良²

1. School of Mathematical Sciences, University of Jinan, Jinan 250022, China;
2. School of Mathematical Sciences, University of Jinan, Jinan 250022, China

收稿日期:2013-01-05 修回日期:2014-05-27 出版日期:2015-03-20 发布日期:2015-03-20
基金资助:
The first author is supported by the Doctoral foundation of University of Jinan (XBS1213) and the National Natural Science Foundation of China (11101242).

A MAXIMUM PRINCIPLE APPROACH TO STOCHASTIC H₂/H_∞ CONTROL WITH RANDOM JUMPS

Qixia ZHANG¹, Qiliang SUN²

1. School of Mathematical Sciences, University of Jinan, Jinan 250022, China;
2. School of Mathematical Sciences, University of Jinan, Jinan 250022, China

Received:2013-01-05 Revised:2014-05-27 Online:2015-03-20 Published:2015-03-20
Supported by:
The first author is supported by the Doctoral foundation of University of Jinan (XBS1213) and the National Natural Science Foundation of China (11101242).

摘要/Abstract

摘要：

A necessary maximum principle is given for nonzero-sum stochastic differential games with random jumps. The result is applied to solve the H₂/H_∞ control problem of stochastic systems with random jumps. A necessary and sufficient condition for the existence of a unique solution to the H₂/H_∞ control problem is derived. The resulting solution is given by the solution of an uncontrolled forward backward stochastic differential equation with random jumps.

关键词: Nonzero-sum stochastic differential games, maximum principle, Poisson process, stochastic H₂/H_∞ control, forward backward stochastic differential equa-tions

Abstract:

Key words: Nonzero-sum stochastic differential games, maximum principle, Poisson process, stochastic H₂/H_∞ control, forward backward stochastic differential equa-tions

中图分类号:

91A15

张启侠, 孙启良. A MAXIMUM PRINCIPLE APPROACH TO STOCHASTIC H₂/H_∞ CONTROL WITH RANDOM JUMPS[J]. 数学物理学报(英文版), 2015, 35(2): 348-358.

Qixia ZHANG, Qiliang SUN. A MAXIMUM PRINCIPLE APPROACH TO STOCHASTIC H₂/H_∞ CONTROL WITH RANDOM JUMPS[J]. Acta mathematica scientia,Series B, 2015, 35(2): 348-358.

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A MAXIMUM PRINCIPLE APPROACH TO STOCHASTIC H₂/H_∞ CONTROL WITH RANDOM JUMPS

A MAXIMUM PRINCIPLE APPROACH TO STOCHASTIC H₂/H_∞ CONTROL WITH RANDOM JUMPS

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