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An ℒ2 disturbance attenuation solution to the nonlinear benchmark problem

✍ Scribed by Panagiotis Tsiotras; Martin Corless; Mario A. Rotea

Publisher: John Wiley and Sons
Year: 1998
Tongue: English
Weight: 426 KB
Volume: 8
Category: Article
ISSN: 1049-8923
DOI: 10.1002/(sici)1099-1239(19980415/30)8:4/5<311::aid-rnc357>3.0.co;2-f

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✦ Synopsis

In this paper, we use the theory of L disturbance attenuation for linear (H ) and nonlinear systems to obtain solutions to the nonlinear benchmark problem (NLBP) proposed in the paper by Bupp et al. By considering a series expansion solution to the Hamilton-Jacobi-Isaacs equation associated with the nonlinear disturbance attenuation problem, we obtain a series expansion solution for a nonlinear controller. Numerical simulations compare the performance of the third-order approximation of the nonlinear controller with its first-order approximation (which is the same as the linear H controller obtained from the linearized problem.

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ADDENDUM: Volume 163, Number 2 (2000), in the article “Effect of Symmetry to the Structure of Positive Solutions in Nonlinear Eliptic Problems,” by Jaeyoung Byeon, pages 429–474 ()

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On p. 429, the title should read ``In Nonlinear Elliptic Problems.'' In addition, the proof of the following lemma, stated on p. 452, requires revision: Lemma 4.5. For a nonnegative minimizer u R of 1 R, M , it holds that, for any $>0 and Correction of the Proof. Suppose that our claim is false. Th