Filtering and Smoothing in an H∞ Setting

IEEE Transactions on Automatic Control

Volumn 36, Issue 2, 1991, Pages 152-166

  Nagpal, Krishan M ^a   Khargonekar, Pramod P ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONTROL SYSTEMS, TIME VARYING; MATHEMATICAL TECHNIQUES - ALGORITHMS; OPTIMIZATION - APPLICATIONS;

FINITE HORIZON CASE; INFINITE HORIZON CASE; INITIAL CONDITIONS; LINEAR TIME INVARIANT SYSTEMS; OPTIMAL SMOOTHER;

CONTROL SYSTEMS, LINEAR;

EID: 0026107390     PISSN: 00189286     EISSN: 15582523     Source Type: Journal    
DOI: 10.1109/9.67291     Document Type: Article

References (26)

1. B. D. O. Anderson and J. B. Moore, “Detectability and stabilizability of time-varying discrete-time linear systems,” SIAM J. Contr. Optimiz., vol. 19, pp. 20-32, 1981.
2. D. S. Bernstein and W. M. Haddad, “Steady-state Kalman filtering with an H∞, error bound,” Syst. Contr. Lett., vol. 12, 9-16, 1989.
3. S. Boyd, V. Balakrishnan, and P. Kabamba, “A bisection method for computing the H∞ of a transfer matrix and related problems,” Math. Contr. Signals Syst., vol. 2, no. 3, pp. 207-219, 1989.
4. R. W. Brockett, Finite Dimensional Linear Systems. New York: Wiley, 1969.
5. J. C. Doyle, K. Glover, P. P. Khargonekar, and B. A. Francis, “State-space solutions to standard H2 and H∞ control problems,” IEEE Trans. Automat. Contr., vol. 34, no. 8, pp. 831-847, 1989.
6. A. Elsayed and M. J. Grimble, “A new approach to design of optimal digital linear filters,” IMA J. Math. Contr. Informat., vol. 6, no. 8, pp. 233-251, 1989.
7. B. A. Francis, A Course in H∞ Control Theory. New York: Springer-Verlag, 1987.
8. D. C. Fraser, “A new technique for optimal smoothing of data,” Ph.D. dissertation, Dept. Aeronautics and Astronautics, Mass. Inst. Technol., Cambridge, MA, 1967.
9. M. J. Grimble, “Minimax design of optimal linear filters,” presented at IFAC Symp., Glasgow, U.K., April 1989.
10. M. J. Grimble, D. Ho, and A. Elsayed, “H∞ robust linear estimator,” presented at MTNS Conf., AZ, 1987.
11. W. M. Haddad and D. S. Berstein, “Optimal reduced-order subspace-observer design with a frequency-domain error bound,” Control and Dynamic Systems, Vol. 32, C. T. Leondes, Ed., New York: Academic, 1990, pp. 23-38.
12. T. Kailath and L. Ljung, “Two filter smoothing formulae by diagonalization of the Hamiltonian equations,” Int. J. Contr., vol. 36, no. 4, pp. 663-673, 1982.
13. A. J. Krener, “Kalman-Bucy and minimax filtering,” IEEE Trans. Automat. Contr., vol. AC-25, no. 2, pp. 291-292, 1980.
14. E. B. Lee and L. Markus, Foundations of Optimal Control Theory. New York: Wiley, 1967.
15. D. J. N. Limebeer, B. D. O. Anderson, P. P. Khargonekar, and M. Green, “A game theoretic approach to the H∞ optimal control of linear time-varying plants,” SIAM J. Contr. Optimize submitted for publication.
16. D. Q. Mayne, “A solution of the smoothing problem for linear dynamic systems,” Automatica, vol. 4, pp. 73-92, 1966.
17. B. P. Molinari, “The stable regulator problem and its inverse,” IEEE Trans. Automat. Contr., vol. 18, no. 10, pp. 454-459, 1990.
18. R. Ravi, K. M. Nagpal, and P. P. Khargonekar, “H∞ control of linear time-varying systems: A state space approach,” College of Engineering, The University of Michigan, Ann Arbor, Contr. Group Rep. No. CGR-43; also submitted for publication.
19. R. Ravi, A. M. Pascoal, and P. P. Khargonekar, “Normalized coprime factorizations and the graph metric for linear time-varying systems,” submitted for publication.
20. W. Rudin, Functional Analysis, New York: McGraw-Hill, 1973.
21. U. Shaked, “H∞ minimum error state estimation of linear stationary processes,” IEEE Trans. Automat. Contr., vol. 35, no. 5, 554-558, 1990.
22. G. Tadmor, “Worst case design in the time domain: The maximum principle and the standard H∞ problem,” Math. Contr. Signals, Syst., to be published.
23. H. L. Weinert, “On the inversion of linear systems,” IEEE Trans. Automat. Contr., vol. AC-29, no. 10, pp. 956-958, 1984.
24. J. C. Willems, “Least-squares stationary optimal control and the algebraic Riccati equation,” IEEE Trans. Automat. Contr., vol. AC-16, no. 8, pp. 621-634, 1971.
25. I. Yaesh and U. Shaked, “Game theory approach to optimal linear estimation in the minimum H∞ norm sense,” in Proc. 1989 CDC, Tampa FL., 1989.
26. G. Zames, “Feedback and optimal sensitivity: Model reference transformations, multiplicative seminorms, and approximate inverses,” IEEE Trans. Automat. Contr., vol. AC-26, pp. 301-320, 1981.