Nonlinear H∞ Optimization: A Causal Power Series Approach

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Title: Nonlinear H∞ Optimization: A Causal Power Series Approach
Author: Foias, Ciprian ; Gu, Caixing ; Tannenbaum, Allen R.
Abstract: In this paper, using a power series methodology a design procedure applicable to analytic nonlinear plants is described. The technique used is a generalization of the linear H∞ theory. In contrast to previous work on this topic ([Indiana J. Math., 36 (1987), pp. 693–709], [Oper. Theory Adv. Appl., 41 (1989), pp. 255–277], [SIAM J. Control Optim., 27 (1989), pp. 842–860] ), the authors are now able to incorporate explicitly a causality constraint into the theory. In fact, it is shown that it is possible to reduce a causal optimal design problem (for nonlinear systems) to a classical interpolation problem solvable by the commutant lifting theorem [Harmonic Analysis of Operators on Hilbert Space, North-Holland, Amsterdam, 1970], [The Commutant Lifitng Approach to Interpolation Problems, Birkhäuser, Boston, 1990].
Description: ©1995 Society for Industrial and Applied Mathematics. Permalink: DOI: 10.1137/S0363012992236164
Type: Article
ISSN: 0363-0129
Citation: Ciprian Foias, Caixing Gu, and Allen Tannenbaum, "Nonlinear H∞ Optimization: A Causal Power Series Approach," SIAM Journal on Control Optimization, Vol. 33, No. 1 (January 1995) 185-207
Date: 1995-01
Contributor: University of Minnesota. Dept. of Electrical Engineering
Indiana University, Bloomington. Dept. of Mathematics
Publisher: Georgia Institute of Technology
Society for Industrial and Applied Mathematics
Subject: Nonlinear systems
H∞ optimization
Commutant lifting theorem
Interpolation theory
Volterra series

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