H/sup /spl infin// control and estimation with preview-part I: matrix ARE solutions in continuous time

Preview control and fixed-lag smoothing allow a noncausal component in the controller/estimator. Time domain variational analysis is used in a reduction to an open loop differential game, leading to a complete, necessary and sufficient characterization of suboptimal values and an explicit state space design, in terms of a parameterized (nonstandard) algebraic matrix Riccati equation in a general continuous time linear system setting. The solution offers insight into the appropriate structure of the associated Hamiltonian, where the state and co-state are not the usual state of the original dynamic system and that of its adjoint. Rather, the state and co-state are selected to capture the respective lumped effects of initial data and future input selection in the allied game.

[1]  Gjerrit Meinsma,et al.  When does the H∞ fixed-lag smoothing performance saturate for a finite smoothing lag? , 2004, IEEE Trans. Autom. Control..

[2]  E. K. Bender,et al.  Optimum Linear Preview Control With Application to Vehicle Suspension , 1968 .

[3]  J. Speyer,et al.  A game-theoretic approach to a finite-time disturbance attenuation problem , 1991 .

[4]  M. Tomizuka.  Optimal continuous finite preview problem , 1975 .

[5]  Leonid Mirkin,et al.  Yet another H∞ discretization , 2003, IEEE Trans. Autom. Control..

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

[7]  M. E. Halpern,et al.  Preview tracking for discrete-time SISO systems , 1994, IEEE Trans. Autom. Control..

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

[9]  Tongwen Chen,et al.  Design of multirate filter banks by 𝒽∞ optimization , 1995, IEEE Trans. Signal Process..

[10]  Petros G. Voulgaris,et al.  On optimal ℓ∞ to ℓ∞ filtering , 1995, Autom..

[11]  Robert R. Bitmead,et al.  Kalman filtering techniques in speech coding , 1992, [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing.

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

[13]  Akira Kojima,et al.  H∞ performance of preview control systems , 2003, Autom..

[14]  Tongwen Chen,et al.  Design of multirate filter banks by /spl Hscr//sub /spl infin// optimization , 1995 .

[15]  Isaac Yaesh,et al.  Minimum H∞-norm regulation of linear discrete-time systems and its relation to linear quadratic discrete games , 1989 .

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

[17]  Blake Hannaford,et al.  Online improvement of speed and tracking performance on repetitive paths , 1998, IEEE Trans. Control. Syst. Technol..

[18]  Hans Zwart,et al.  An Introduction to Infinite-Dimensional Linear Systems Theory , 1995, Texts in Applied Mathematics.

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

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

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

[22]  Huei Peng,et al.  A unified hamiltonian approach for lq and H∞ preview control algorithms , 1999 .

[23]  Leonid Mirkin,et al.  H∞ control of system with I/O delay: a review of some problem‐oriented methods , 2002 .

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

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

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

[27]  A. K. Mahalanabis,et al.  Improved multi-target tracking in clutter by PDA smoothing , 1990 .

[28]  U. Shaked,et al.  Minimum H/sub infinity /-norm regulation of linear discrete-time systems and its relation to linear quadratic discrete games , 1990 .

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

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

[31]  Leonid Mirkin,et al.  Yet another H/sup /spl infin// discretization , 2003 .

[32]  L. Mirkin,et al.  H/sup /spl infin// control and estimation with preview-part II: fixed-size ARE solutions in discrete time , 2005, IEEE Transactions on Automatic Control.

[33]  C. D. Souza,et al.  Continuous-time tracking problems in an H∞ setting: a game theory approach , 1995, IEEE Trans. Autom. Control..

[34]  Leonid Mirkin,et al.  Yet Another Discretization , 2003 .

[35]  T. Basar,et al.  H∞-0ptimal Control and Related Minimax Design Problems: A Dynamic Game Approach , 1996, IEEE Trans. Autom. Control..