Elsevier

Automatica

Volume 24, Issue 4, July 1988, Pages 485-497
Automatica

Paper
Non-linear dynamics in adaptive control: Periodic and chaotic stabilization—II. Analysis

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Abstract

A particular non-linear equation arising in an adaptive control problem is presented in the first part of this paper. This equation displays vividly a wealth of non-linear phenomena. Depending on the value of one crucial parameter—characterizing the extent and presence of “non-design” circumstances—we demonstrate the existence of asymptotically periodic behaviour or chaotic dynamics in the feedback controller. This paper contains the mathematical analysis associated with the earlier results and, as such, serves two main purposes: to provide the theoretical proofs and support for these results, and to demonstrate more fully the extraordinary complexity and difficulty of conducting a thorough global analysis of even this simplest of robust adaptive problems. By performing this latter task we aim to delineate better what are reasonable objectives to be expected of robust adaptive control theory.

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The original version of this paper was not presented at any IFAC meeting. This paper was recommended for publication in revised form by Associate Editor G. Kreisselmeier under the direction of Editor P. C. Parks.

1

Current address: Department of Electrical and Computer Engineering, University of Newcastle, NSW 2308, Australia.

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