Stochastic H2/H ∞ control with (x,u,v)-dependent noise: Finite horizon case

  • Authors:

  • Weihai Zhang;Huanshui Zhang;Bor-Sen Chen

  • Affiliations:

  • College of Information and Electrical Engineering, Shandong University of Science and Technology, Qingdao 266510, PR China and School of Electronic Information and Control Engineering, Shandong In ...;Shenzhen Graduate School of Harbin Institute of Technology, HIT Campus, Shenzhen University Town, Xili, Shenzhen 518055, PR China;Department of Electrical Engineering, National Tsing Hua University, Hsinchu 30013, Taiwan, PR China

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2006

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Abstract

In this paper, the finite horizon mixed H"2/H"~ control problem is studied for the systems governed by Ito-type nonlinear stochastic differential equations with state, control and external disturbance-dependent noise. It is shown that the mixed H"2/H"~ control under consideration is associated with the four cross-coupled Hamilton-Jacobi equations. A discrete approximation algorithm is presented for solving the coupled generalized differential Riccati equations arising from linear stochastic H"2/H"~ control. A necessary condition and a sufficient condition for the existence of the finite horizon stochastic H"2/H"~ control are derived. In particular, some previous results on deterministic and stochastic H"2/H"~ control can be viewed as corollaries of our main theorems.