NDLI: Unstable systems stabilizing each other through adaptation

Content Provider	IEEE Xplore Digital Library
Author	Narendra, K.S. Harshangi, P.
Copyright Year	2015
Description	Author affiliation: Center for Syst. Sci., Yale Univ., New Haven, CT, USA (Narendra, K.S.; Harshangi, P.)
Abstract	It is now well realized [1] that two unstable dynamical systems, attempting to stabilize each other using the error between their outputs for adjusting their parameters, may not always succeed. The fact that adaptation may result in instability makes the mathematical problem a very interesting one. Since similar problems are arising in many other branches of science (e.g psychology, biology, medicine etc), obtaining precisely the conditions under which stability is achieved is also assuming greater importance. This paper may be considered as a first attempt to discuss the many aspects of this intriguing and difficult problem. Work carried out during the past year has shown that the interaction of two $n^{th}$ order systems, results in a $4n^{th}$ order differential equation, whose stability has to be investigated. Even in the simple case when n = 2, determining necessary and sufficient conditions for stability is a formidable undertaking. However, through extensive simulation studies and the theoretical analysis of special cases suggested by them, numerous insights have been obtained. The objective of this paper is to convey these insights, and discuss wherever possible, their implications to higher order systems.
Starting Page	856
Ending Page	861
File Size	440283
Page Count	6
File Format	PDF
e-ISBN	9781479986842
DOI	10.1109/ACC.2015.7170841
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-07-01
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	American Automatic Control Council(AACC)
Subject Keyword	Eigenvalues and eigenfunctions Stability analysis Mathematical model Adaptive systems Adaptation models Trajectory Differential equations
Content Type	Text
Resource Type	Article

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