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International Journal of Control Volume 24, 1976 - Issue 6
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Original Articles

A general transfer-function approach to the steady-state linear quadratic Gaussian stochastic control problem

U. SHAKED Control and Management Systems Group, Engineering Department, University of Cambridge, England
Pages 771-800 | Received 10 Jun 1976, Published online: 24 Oct 2007

Citations (53)

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A. CASAVOLA, M. J. GRIMBLE & E. MOSCA. (1996) Extensions to generalized LQG and H multivariable controllers. International Journal of Control 63:3, pages 507-517.
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M. J. GRIMBLE. (1995) H/ H∞ robust control design for a generalized control structure and flight control application. International Journal of Systems Science 26:11, pages 2043-2068.
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HUEI PENG, WEIBIN ZHANG, MASAYOSHI TOMIZUKA & STEVEN SHLADOVER. (1994) A Reusability Study of Vehicle Lateral Control System. Vehicle System Dynamics 23:1, pages 259-278.
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KIHEON PARK & DANTEC. YOULA. (1992) Numerical calculation of the optimal three-degree-of-freedom Wiener-Hopf controller. International Journal of Control 56:1, pages 227-244.
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MARCOS AZEVEDO DA SILVEIRA & GILBERTOOLIVEIRA CORRÊA. (1992) H2-optimal control of linear systems with tracking/disturbance rejection constraints. International Journal of Control 55:5, pages 1115-1139.
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M. J. GRIMBLE. (1991) Polynomial matrix solution to the standard H 2 optimal control problem. International Journal of Systems Science 22:5, pages 793-806.
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A. CASAVOLA. (1991) Polynomial solution of the continuous-time GMV control problem. International Journal of Control 53:3, pages 641-660.
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M. J. GRIMBLE. (1990) Pole-zero cancellation problem in the convergence of explicit LQG self-tuning controllers. International Journal of Systems Science 21:8, pages 1409-1422.
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M. J. GRIMBLE. (1990) Design procedure for combined H∞ and LQG cost problem. International Journal of Systems Science 21:1, pages 93-127.
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M. J. GRIMBLE. (1989) Extensions to H∞ multivariable robust controllers and the relationship to LQG design problems. International Journal of Control 50:1, pages 309-338.
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KJELL NORDSTROM†. (1987) Trade-off between noise sensitivity and robustness for LQG regulators. International Journal of Control 46:5, pages 1689-1714.
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M. J. GRIMBLE. (1987) H ∞ robust controller for self-tuning control applications Part 1. Controller design. International Journal of Control 46:4, pages 1429-1444.
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M. J. GRIMBLE. (1986) Optimal H∞ robustness and the relationship to LQG design problems. International Journal of Control 43:2, pages 351-372.
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CHARLES CASTEL & CLAUDE REBOULET. (1983) Algebraic approach to stochastic optimal digital controller design. International Journal of Control 37:5, pages 1145-1157.
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M. J. GRIMBLE. (1979) Solution of the discrete-time stochastic optimal control problem in the 2-domain. International Journal of Systems Science 10:12, pages 1369-1390.
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Articles from other publishers (38)

T.J. Moir. (2022) A study on square root control-systems. Journal of Computational and Applied Mathematics 406, pages 113938.
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T. J. Moir. (2022) Polynomial Wiener LQG Controllers based on Toeplitz Matrices. Journal of Physics: Conference Series 2224:1, pages 012114.
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Michael J. Grimble & Paweł MajeckiMichael J. Grimble & Paweł Majecki. 2020. Nonlinear Industrial Control Systems. Nonlinear Industrial Control Systems 291 344 .
Michael J. Grimble & Paweł MajeckiMichael J. Grimble & Paweł Majecki. 2020. Nonlinear Industrial Control Systems. Nonlinear Industrial Control Systems 65 125 .
Hongguo Zhao, Huanshui Zhang, Hongxia Wang & Chenghui Zhang. (2008) Linear Quadratic Regulation for Discrete-Time Systems with Input Delay: Spectral Factorization Approach. Journal of Systems Science and Complexity 21:1, pages 46-59.
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Michael J. Grimble. 2006. Robust Industrial Control Systems. Robust Industrial Control Systems 469 528 .
Michael J. Grimble. 2006. Robust Industrial Control Systems. Robust Industrial Control Systems 299 387 .
Michael J. Grimble. 2006. Robust Industrial Control Systems. Robust Industrial Control Systems 167 247 .
Michael J. Grimble. 2006. Robust Industrial Control Systems. Robust Industrial Control Systems 57 111 .
M. J. Grimble. (2003) Discrete‐time polynomial systems approach to combined fault monitoring and control. Optimal Control Applications and Methods 24:3, pages 121-138.
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M. J. Grimble. (2002) Polynomial matrix solution of H 2 optimal control problem for state‐space systems . Optimal Control Applications and Methods 23:2, pages 59-89.
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M. A. Da Silveira & R. Ades. (2002) The Solution of the $\mbox\boldmath$H^2/H^\infty$$ Problem by Direct Methods. SIAM Journal on Control and Optimization 41:4, pages 1089-1117.
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M. J. Grimble. (2001) Restricted structure control of multiple model systems with Series 2 DOF tracking and feedforward action. Optimal Control Applications and Methods 22:4, pages 157-196.
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M. J. Grimble. (1999) Polynomial solution of the 3 1/2-DOF H2/H∞ feedforward control problem. IEE Proceedings - Control Theory and Applications 146:6, pages 549-560.
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M.J. Grimble. (1998) LQG controllers for discrete-time multivariable systems with different transport delays in signal channels. IEE Proceedings - Control Theory and Applications 145:5, pages 449-462.
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M.J. Grimble. (1998) Combined fault monitoring detection and control. Combined fault monitoring detection and control.
M. J. Grimble. (1995) POLYNOMIAL SOLUTION OF THE STANDARD H 2 OPTIMAL CONTROL PROBLEM FOR MACHINE CONTROL SYSTEM APPLICATIONS: LQG GAUGE CONTROL PROBLEM DESIGN . Optimal Control Applications and Methods 16:2, pages 77-104.
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M.J. Grimble. (1995) Multivariable linear quadratic generalized predictive control. Multivariable linear quadratic generalized predictive control.
M.J. Grimble. (1994) Two and a half degrees of freedom LQG controller and application to wind turbines. IEEE Transactions on Automatic Control 39:1, pages 122-127.
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I.H. Noell, P.C. Austin & M.R. Carter. (1993) Linear Quadratic Gaussian Controllers for Perfect Measurements. IFAC Proceedings Volumes 26:2, pages 431-434.
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S. Baṅka. (2007) Multipurpose controller design in multivariable stochastic control systems. Optimal Control Applications and Methods 12:2, pages 89-118.
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D. Fragopoulos, M.J. Grimble & U. Shaked. (1991) H/sub infinity / controller design for the SISO case using a Wiener approach. IEEE Transactions on Automatic Control 36:10, pages 1204-1208.
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M.J. Grimble. (1991) H/sub infinity / fixed-lag smoothing filter for scalar systems. IEEE Transactions on Signal Processing 39:9, pages 1955-1963.
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M.J. Grimble. (1990) LQG predictive optimal control for adaptive applications. Automatica 26:6, pages 949-961.
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M.J. Grimble & D. Fragopoulos. (1990) Solution of discrete H/sub infinity / optimal control problems using a state-space approach. Solution of discrete H/sub infinity / optimal control problems using a state-space approach.
M.J. Grimble. (1989) Minimization of a combined H∞ and LQG cost-function for a two-degrees-of-freedom control design. Automatica 25:4, pages 635-638.
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K. Park & J.J. Bongiorno. (1989) A general theory for the Wiener-Hopf design of multivariable control systems. IEEE Transactions on Automatic Control 34:6, pages 619-626.
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Y. Halevi & Z.J. Palmor. (1988) Admissible MIMO singular observation LQG designs. Automatica 24:1, pages 43-51.
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John B. Moore & D.L. Mingori. (1987) Robust frequency-shaped LQ control. Automatica 23:5, pages 641-646.
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G. Stein & M. Athans. (1987) The LQG/LTR procedure for multivariable feedback control design. IEEE Transactions on Automatic Control 32:2, pages 105-114.
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Peter M. Thompson. (2007) Program CC's implementation of the wiener‐hopf lqg optimal control problem. Optimal Control Applications and Methods 8:1, pages 63-89.
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Y. Halevi & Z. J. Palmor. (2006) Inadmissibility of siso singular observation lqg design. Optimal Control Applications and Methods 7:3, pages 219-241.
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B. D. O. Anderson & D. L. Mingori. (1985) Use of frequency dependence in linear quadratic control problems to frequency-shape robustness. Journal of Guidance, Control, and Dynamics 8:3, pages 397-401.
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J.B. Moore, B.D.O. Anderson & D.L. Mingori. (1984) Frequency Shaped Linear Optimal Control with Transfer Function Riccati Equations. IFAC Proceedings Volumes 17:2, pages 287-292.
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M.J. Grimble. (2016) Design of closed-loop optimal controllers for systems with shape deterministic inputs. Transactions of the Institute of Measurement and Control 3:2, pages 79-88.
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M. Safonov, A. Laub & G. Hartmann. (1981) Feedback properties of multivariable systems: The role and use of the return difference matrix. IEEE Transactions on Automatic Control 26:1, pages 47-65.
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M. J. Grimble. (2006) A combined state and state estimate feedback solution to the ship positioning control problem. Optimal Control Applications and Methods 1:1, pages 55-67.
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Vladimír Kučera. (1979) Design of steady-state minimum variance controllers. Automatica 15:4, pages 411-418.
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