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Degenerate Gradient Flows: A Comparison Study of 1Convergence Rate Estimates

Summary: Degenerate Gradient Flows: A Comparison Study of
1Convergence Rate Estimates
S. Andersson and P. S. Krishnaprasad
Electrical and Computer Engineering and Institute for Systems Research
University of Maryland, College Park, MD 20742
{sanderss, krishna} @glue.umd.edu
Degenerate gradient flows arise in the context of adap-
tive control of linear systems when the usual gradient
algorithm is used for the parameter update law. It
is well known that in general parameter convergence is
not guaranteed without further assumptions. The start-
dard approach utilizes the notion of a persistently ex-
citing input and different authors have derived different
convergence rate estimates. In a recent paper Brockett
re-examined this issue and developed a rate estimate
using a property of symmetric matrices related to the
condition number. In this paper we compare two well-
known convergence rate estimates from the persistently
exciting point of view with Brockett's estimate through


Source: Andersson, Sean B. - Department of Aerospace and Mechanical Engineering, Boston University


Collections: Engineering