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Linear estimation in Krein spaces. Part II. Applications

Hassibi, Babak and Sayed, Ali H. and Kailath, Thomas (1996) Linear estimation in Krein spaces. Part II. Applications. IEEE Transactions on Automatic Control, 41 (1). pp. 34-49. ISSN 0018-9286. doi:10.1109/9.481606.

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We have shown that several interesting problems in H∞-filtering, quadratic game theory, and risk sensitive control and estimation follow as special cases of the Krein-space linear estimation theory developed in Part I. We show that all these problems can be cast into the problem of calculating the stationary point of certain second-order forms, and that by considering the appropriate state space models and error Gramians, we can use the Krein-space estimation theory to calculate the stationary points and study their properties. The approach discussed here allows for interesting generalizations, such as finite memory adaptive filtering with varying sliding patterns.

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Additional Information:© 1996 IEEE. Reprinted with permission. Manuscript received March 4, 1994; revised June 16, 1995. Recommended by Associate Editor at Large, B. Pasik-Duncan. This work was supported in part by the Air Force Office of Scientific Research, Air Force Systems Command under Contract AFOSR91-0060, in part by the Army Research Office under Contract DAAL03-89-K-0109, and in part by a grant from NSF under award MIP-9409319. The authors would like to thank P. P. Khargonekar and D. J. N. Limebeer for helpful discussions during the preparation of this manuscript. Seminars by P. Park on the KYP Lemma were also helpful in leading us to begin the research.
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Air Force Office of Scientific Research (AFOSR)AFOSR91-0060
Army Research Office (ARO)DAAL03-89-K-0109
Subject Keywords:H∞ control, Kalman filters, adaptive filters, filtering theory, recursive estimation, state estimation, state-space methods
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Record Number:CaltechAUTHORS:HASieeetac96b
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2240
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Deposited On:17 Mar 2006
Last Modified:08 Nov 2021 19:46

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