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Upper bounds for mixed H^2/H^∞ control

Hassibi, Babak and Kailath, Thomas (1998) Upper bounds for mixed H^2/H^∞ control. In: Proceedings of the 37th IEEE Conference on Decision and Control, 1998. Vol.1. IEEE , Piscataway, NJ, pp. 652-657. ISBN 0-7803-4394-8. https://resolver.caltech.edu/CaltechAUTHORS:20150217-075137959

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Abstract

We consider the mixed H^2/H^∞ control problem of choosing a controller to minimize the H^2 norm of a given closed-loop map, subject to the H^∞ norm of another closed-loop map being less than a prescribed value γ. Let d_2 and γ_2 denote the H^2 and H^∞ norms for the pure H^2-optimal solution (without any H^∞ constraint), and let d_c and γ_c < γ denote the H^2 and H^∞ norms for any solution that yields an H^∞ norm strictly less than γ (such as, say, the central solution). Then if d_m denotes the optimal H2 norm that can be achieved in the mixed H^2/H^∞ control problem, we show that (d^2_m - d^2_2)/(d^_c - d^2_2) ⩽ ((γ_2 - γ)/(γ_2 - γ_c))^2 < ((γ^2_2 - γ^2)/(γ^2_2 - γ^2_c))^2 < 1.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1109/CDC.1998.760757DOIArticle
http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=760757PublisherArticle
Additional Information:© 1998 IEEE. This work was supported in part by DARPA through the Department of Air Force under contract F49620-95-1-0525-P00001 and by the Joint Service Electronics Program at Stanford under contract DAAH04-94-G-0058-P00003.
Funders:
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)F49620-95-1-0525-P00001
Joint Service Electronics ProgramDAAH04-94-G-0058-P00003
Defense Advanced Research Projects Agency (DARPA)UNSPECIFIED
Record Number:CaltechAUTHORS:20150217-075137959
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20150217-075137959
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ID Code:54851
Collection:CaltechAUTHORS
Deposited By: Shirley Slattery
Deposited On:28 Feb 2015 03:25
Last Modified:03 Oct 2019 08:01

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