On non-local stability properties of extremum seeking control

By Ying Tan, Dragan Nesic, Iven M. Y. Mareels. at - Automatisierungstechnik, 2006

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Multivariable Newton-based extremum seeking (2011, background): “We can also prove non–local stability of the proposed scheme in a similar manner as [19] where gradient–based algorithm was investigated.”
Extremum seeking from 1922 to 2010 (2010, background): “To ensure that the notion of a steady state is well defined, the following assumptions may be imposed, see also [150].”
Technical communique: On the choice of dither in extremum seeking systems: A case study (2008, neutral): “Although this method dates back to the early 1950's and 1960's, the first rigorous local stability analysis for an ES scheme was recently proved in Krsti´c and Wang (2000) and later extended to semi-global stability analysis in Tan, Neši´c, and Mareels (2005, 2006).”
Distributed Seeking of Nash Equilibria With Applications to Mobile Sensor Networks (2012, background): “…recently proposed algorithms in [13] and [14] deal with an information structure similar to the one imposed in this paper, but require synchronization between the agents, and the convergence is proved only for a special class of games (weakly acyclic or potential games [4]) with finite action sets.”
Nash Equilibrium Seeking in Noncooperative Games (2012, background): “Then, the Nash equilibrium is semi-globally practically asymptotically stable.”