Linear Quadratic Regulation for Discrete-Time Systems with Input Delay: Spectral Factorization Approach

The infinite-horizon linear quadratic regulation (LQR) problem is settled for discrete-time systems with input delay. With the help of an autoregressive moving average (ARMA) innovation model, solutions to the underlying problem are obtained. The design of the optimal control law involves in resolving one polynomial equation and one spectral factorization. The latter is the major obstacle of the present problem, and the reorganized innovation approach is used to clear it up. The calculation of spectral factorization finally comes down to solving two Riccati equations with the same dimension as the original systems.

[1]  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.

[2]  K. Åström.  Introduction to Stochastic Control Theory , 1970 .

[3]  Dong H. Chyung,et al.  Discrete systems with delays in control , 1969 .

[4]  Gjerrit Meinsma,et al.  H2-optimal control of systems with multiple i/o delays: Time domain approach , 2005, Autom..

[5]  Y.C. Soh,et al.  A reorganized innovation approach to linear estimation , 2004, IEEE Transactions on Automatic Control.

[6]  M. Sternad,et al.  A novel derivation methodology for polynomial-LQ controller design , 1993, IEEE Trans. Autom. Control..

[7]  L. Mirkin,et al.  H/sup /spl infin// control of systems with multiple I/O delays via decomposition to adobe problems , 2005, IEEE Transactions on Automatic Control.

[8]  Michael Sebek,et al.  Optimal regulation using measurement feedback: a polynomial approach , 1992 .

[9]  B. Nicoletti,et al.  Optimal discrete systems with pure delays , 1973 .

[10]  David Zhang,et al.  Hinfinity Fixed-lag smoothing for discrete linear time-varying systems , 2005, Autom..

[11]  M. Delfour.  The linear quadratic optimal control problem with delays in state and control variables: a state space approach , 1986 .

[12]  Luigi Chisci,et al.  MMSE deconvolution via polynomial methods and its dual LQG regulation , 1994, Autom..

[13]  Guang-Ren Duan,et al.  Linear quadratic regulation for linear time-varying systems with multiple input delays part II: continuous-time case , 2006, 2005 International Conference on Control and Automation.

[14]  Vladimír Kucera,et al.  Discrete linear control: The polynomial equation approach , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[15]  Jon H. Davis,et al.  Foundations of Deterministic and Stochastic Control , 2002 .

[16]  Uri Shaked,et al.  A general transfer-function approach to the steady-state linear quadratic Gaussian stochastic control problem , 1976 .