Variance-constrained multiobjective filtering for uncertain continuous-time stochastic systems

In this paper, we consider stochastic linear continuous-time systems subject to parameter uncertainties affecting both system dynamics and noise statistics. A linear filter is used to estimate a linear combination of the states of the system. The problem addressed is the design of a perturbation-independent filter such that, for all admissible parameter perturbations, the following three objectives are simultaneously achieved. Firstly the filtering process is D-stable, that is, the eigenvalues of the filtering matrix are located inside a prespecified disc. Secondly the steady-state variance of the estimation error of each state is not more than the individual prespecified value. Thirdly the transfer function from exogenous noise inputs to error state outputs meets the prespecified H norm upper bound constraint. Therefore, the resulting filtering process will be provided with the expected transient property, steady-state error variance constraint and disturbance rejection behaviour, irrespective of the parameter uncertainties. An effective algebraic matrix inequality approach is developed to solve such a multiobjective H2

[1]  Ian R. Petersen,et al.  Quadratic guaranteed cost control with robust pole placement in a disk , 1996 .

[2]  Robert E. Skelton,et al.  Design of covariance controllers and estimators with prescribed pole locations , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[3]  Lihua Xie,et al.  H∞ estimation for uncertain systems , 1992 .

[4]  J. Willems.  Least squares stationary optimal control and the algebraic Riccati equation , 1971 .

[5]  E. Yaz,et al.  Linear and nonlinear estimation with uncertain observations , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[6]  Karolos M. Grigoriadis,et al.  Robust regional pole assignment with output feedback , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[7]  D. McFarlane,et al.  Optimal guaranteed cost filtering for uncertain discrete-time linear systems , 1996 .

[8]  C. Scherer,et al.  Multiobjective output-feedback control via LMI optimization , 1997, IEEE Trans. Autom. Control..

[9]  Wei-Yong Yan,et al.  Design of low-order linear-phase IIR filters via orthogonal projection , 1999, IEEE Trans. Signal Process..

[10]  D. Bernstein,et al.  Steady-state Kalman filtering with an H ∞ error bound , 1989 .

[11]  G. Papavassilopoulos,et al.  A global optimization approach for the BMI problem , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[12]  U. Shaked,et al.  H,-OPTIMAL ESTIMATION: A TUTORIAL , 1992 .

[13]  Uri Shaked,et al.  Robust minimum variance filtering , 1995, IEEE Trans. Signal Process..

[14]  R. Skelton,et al.  Liapunov and Covariance Controllers , 1992, 1992 American Control Conference.

[15]  E. Yaz,et al.  Nonlinear Estimation by Covariance Assignment , 1993 .

[16]  G. Nicolao,et al.  Optimal robust filtering with time-varying parameter uncertainty , 1996 .

[17]  E. Yaz,et al.  Continuous and discrete state estimation with error covariance assignment , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[18]  K. Grigoriadis,et al.  A Combined Alternating Projections and Semidefinite Programming Algorithm for Low-Order Control Design , 1996 .

[19]  Wang Zidong,et al.  Robust controller design for uncertain linear systems with circular pole constraints , 1996 .