On the Hinfinity fixed-lag smoothing: how to exploit the information preview

The problem of the continuous-time H^~ fixed-lag smoothing over the infinite horizon is studied. The first solution to the problem is derived in terms of one algebraic Riccati equation of the same dimension as in the filtering case and the mechanism by which the performance improvements with respect to the H^~ filtering occur is clarified. It is shown that the H^~ smoother exploits the information preview in an ''H^2 manner''.

[1]  J. Doyle,et al.  Robust and optimal control , 1995, Proceedings of 35th IEEE Conference on Decision and Control.

[2]  Pascal Gahinet,et al.  On the game Riccati equations arising in H/sub infinity / control problems , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[3]  Michael J. Grimble,et al.  H∞ fixed-lag smoothing filter for scalar systems , 1991, IEEE Trans. Signal Process..

[4]  Patrizio Colaneri,et al.  H/sub /spl infin// prediction and smoothing for discrete-time systems: a J-spectral factorization approach , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[5]  Hans Zwart,et al.  On 𝒽∞ control for dead-time systems , 2000, IEEE Trans. Autom. Control..

[6]  Hans Zwart,et al.  On /spl Hscr//sub /spl infin// control for dead-time systems , 2000 .

[7]  B. Anderson,et al.  Optimal Filtering , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[8]  P. Khargonekar,et al.  Filtering and smoothing in an H/sup infinity / setting , 1991 .

[9]  Lihua Xie,et al.  H∞ deconvolution filtering, prediction, and smoothing: a Krein space polynomial approach , 2000, IEEE Trans. Signal Process..

[10]  Gjerrit Meinsma,et al.  Unstable and nonproper weights in H∞ control , 1995, Autom..

[11]  Pascal Gahinet,et al.  On the Game Riccati Equations Arising in $H_\infty$ Control Problems , 1994 .

[12]  Uri Shaked,et al.  Game theory approach to H∞-optimal discrete-time fixed-point and fixed-lag smoothing , 1994, IEEE Trans. Autom. Control..

[13]  Pramod P. Khargonekar,et al.  FILTERING AND SMOOTHING IN AN H" SETTING , 1991 .

[14]  T. Kailath,et al.  Indefinite-quadratic estimation and control: a unified approach to H 2 and H ∞ theories , 1999 .

[15]  Leonid Mirkin.  Continuous-time fixed-lag smoothing in an H/sup /spl infin// setting , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[16]  Hans Zwart,et al.  J-spectral factorization and equalizing vectors , 2001, Syst. Control. Lett..

[17]  Leonid Mirkin,et al.  On the extraction of dead-time controllers and estimators from delay-free parametrizations , 2003, IEEE Trans. Autom. Control..

[18]  Carsten W. Scherer,et al.  H/sub infinity /-control by state-feedback and fast algorithms for the computation of optimal H/sub infinity /-norms , 1990 .

[19]  Norbert Wiener,et al.  Extrapolation, Interpolation, and Smoothing of Stationary Time Series , 1964 .