H/sup /spl infin// control and estimation with preview-part II: fixed-size ARE solutions in discrete time

H/sup /spl infin// preview control and fixed-lag smoothing problems are solved in general discrete time linear systems, via a reduction to equivalent open-loop differential games. To prevent high order Riccati equations, found in some solutions, the state of the Hamilton-Jacobi system resides in a quotient space of an auxiliary extended state space system. The dimension of that auxiliary space is equal to the state space dimension of the original system (ignoring the delay).

[1]  Patrizio Colaneri,et al.  A -spectral factorization approach for H∞ estimation problems in discrete time , 2002, IEEE Trans. Autom. Control..

[2]  L. Mirkin,et al.  Fixed-lag smoothing as a constrained version of the fixed-interval case , 2004, Proceedings of the 2004 American Control Conference.

[3]  Anton A. Stoorvogel,et al.  The H ∞ control problem: a state space approach , 2000 .

[4]  Dietmar A. Salamon,et al.  On control and observation of neutral systems , 1982 .

[5]  Lihua Xie,et al.  A unified approach to linear estimation for discrete-time systems. II. H/sub /spl infin// estimation , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[6]  Leonid Mirkin,et al.  On the Hinfinity fixed-lag smoothing: how to exploit the information preview , 2003, Autom..

[7]  Fernando Paganini,et al.  IEEE Transactions on Automatic Control , 2006 .

[8]  G. Tadmor.  Robust control in the gap: a state-space solution in the presence of a single input delay , 1997, IEEE Trans. Autom. Control..

[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.  When does the H∞ fixed-lag smoothing performance saturate for a finite smoothing lag? , 2004, IEEE Trans. Autom. Control..

[11]  Gilead Tadmor,et al.  Worst-case design in the time domain: The maximum principle and the standardH∞ problem , 1990, Math. Control. Signals Syst..

[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]  Akira Kojima,et al.  Robust controller design for delay systems in the gap-metric , 1995, IEEE Trans. Autom. Control..

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

[15]  Allan C. Kahane,et al.  ON THE DISCRETE-TIME H 1 FIXED-LAG SMOOTHING , 2002 .

[16]  Leonid Mirkin,et al.  On the H∞ Fixed-Lag Smoothing: How to Exploit the Information Preview , 2001 .

[17]  Huanshui Zhang,et al.  A unified approach to linear estimation for discrete-time systems. I. H/sub 2/ estimation , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[18]  Patrizio Colaneri,et al.  On discrete-time H∞ fixed-lag smoothing , 2004 .

[19]  Gilead Tadmor,et al.  The standard H ∞ problem and the maximum principle: the general linear case , 1993 .

[20]  Leonid Mirkin,et al.  H/sup /spl infin// control and estimation with preview-part I: matrix ARE solutions in continuous time , 2005, IEEE Transactions on Automatic Control.

[21]  Paolo Bolzern,et al.  H-infinity smoothing in discrete-time: a direct approach , 2002 .

[22]  Michel C. Delfour,et al.  The structural operator F and its role in the theory of retarded systems, II☆ , 1980 .

[23]  Vlad Ionescu,et al.  Generalized Riccati theory and robust control , 1999 .

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

[25]  Michel C. Delfour,et al.  F-reduction of the operator Riccati equation for hereditary differential systems , 1978, Autom..

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