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

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

Abstract

Abstract:

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.

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

CLC Number:

91A15

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

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