H∞ control for stochastic systems with Poisson jumps

This paper discusses the H∞ control problem for a class of linear stochastic systems driven by both Brownian motion and Poisson jumps. The authors give the basic theory about stabilities for such systems, including internal stability and external stability, which enables to prove the bounded real lemma for the systems. By means of Riccati equations, infinite horizon linear stochastic state-feedback H∞ control design is also extended to such systems.

[1]  Weihai Zhang,et al.  State Feedback HINFINITY Control for a Class of Nonlinear Stochastic Systems , 2006, SIAM J. Control. Optim..

[2]  Bor-Sen Chen,et al.  Unified Design for H2, H∞, and Mixed Control of Spacecraft , 1999 .

[3]  Bor-Sen Chen,et al.  Stochastic H2/Hinfinity control with (x, u, v)-dependent noise: Finite horizon case , 2006, Autom..

[4]  B. Anderson,et al.  A game theoretic approach to H ∞ control for time-varying systems , 1992 .

[5]  Bor-Sen Chen,et al.  Attitude Control of Spacecraft: Mixed H/H Approach , 2001 .

[6]  Bor-Sen Chen,et al.  Stochastic H2/H∞ control with state-dependent noise , 2004, IEEE Trans. Autom. Control..

[7]  Raymond Rishel,et al.  A Minimum Principle for Controlled Jump Processes , 1975 .

[8]  M.D.S. Aliyu,et al.  H/sub /spl infin// control for Markovian jump nonlinear systems , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[9]  Xunjing Li,et al.  Necessary Conditions for Optimal Control of Stochastic Systems with Random Jumps , 1994 .

[10]  E. Renshaw,et al.  STOCHASTIC DIFFERENTIAL EQUATIONS , 1974 .

[11]  Vasile Dragan,et al.  Global Solutions to a Game-Theoretic Riccati Equation of Stochastic Control , 1997 .

[12]  Ian R. Petersen,et al.  Absolute Stabilization and Minimax Optimal Control of Uncertain Systems with Stochastic Uncertainty , 1997 .

[13]  Shige Peng,et al.  Stochastic optimization theory of backward stochastic differential equations with jumps and viscosity solutions of Hamilton–Jacobi–Bellman equations , 2009 .

[14]  Zhen Wu,et al.  Fully coupled FBSDE with Brownian motion and Poisson process in stopping time duration , 2003, Journal of the Australian Mathematical Society.

[15]  T. Damm.  State-feedback H∞-type control of linear systems with time-varying parameter uncertainty , 2002 .

[16]  Carl Graham,et al.  McKean-Vlasov Ito-Skorohod equations, and nonlinear diffusions with discrete jump sets , 1992 .

[17]  Vasile Dragan,et al.  The γ-attenuation problem for systems with state dependent noise , 1999 .

[18]  L. Rogers.  Stochastic differential equations and diffusion processes: Nobuyuki Ikeda and Shinzo Watanabe North-Holland, Amsterdam, 1981, xiv + 464 pages, Dfl.175.00 , 1982 .

[19]  José Claudio Geromel,et al.  Output feedback control of Markov jump linear systems in continuous-time , 2000, IEEE Trans. Autom. Control..

[20]  P. Khargonekar,et al.  State-space solutions to standard H/sub 2/ and H/sub infinity / control problems , 1989 .

[21]  V. Ugrinovskii.  Robust H∞ infinity control in the presence of stochastic uncertainty , 1998 .

[22]  D. Hinrichsen,et al.  Stochastic $H^\infty$ , 1998 .

[23]  Situ Rong.  On solutions of backward stochastic differential equations with jumps and applications , 1997 .

[24]  Xiang Chen,et al.  Multiobjective \boldmathHt/Hf Control Design , 2001, SIAM J. Control. Optim..

[25]  Zikuan Liu,et al.  Robust H∞ control of discrete-time Markovian jump linear systems with mode-dependent time-delays , 2001, IEEE Trans. Autom. Control..

[26]  A. V. Skorohod,et al.  The theory of stochastic processes , 1974 .

[27]  P. Varaiya,et al.  Optimal Control of Jump Processes , 1977 .

[28]  Isaac Yaesh,et al.  Robust H∞ filtering of stationary continuous-time linear systems with stochastic uncertainties , 2001, IEEE Trans. Autom. Control..