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Extremum seeking control: a systematic design framework

Title
Extremum seeking control: a systematic design framework
Funding
ARC | Discovery Projects
Contract (GA) number
DP120101144
Start Date
2012/01/01
End Date
2014/12/31
Open Access mandate
no
Organizations
-
More information
http://purl.org/au-research/grants/arc/DP120101144

 

  • Optimization Methods on Riemannian Manifolds via Extremum Seeking Algorithms

    Taringoo, Farzin; Dower, Peter M.; Nesic, Dragan; Tan, Ying (2014)
    Projects: ARC | Extremum seeking control: a systematic design framework (DP120101144)
    This paper formulates the problem of Extremum Seeking for optimization of cost functions defined on Riemannian manifolds. We extend the conventional extremum seeking algorithms for optimization problems in Euclidean spaces to optimization of cost functions defined on smooth Riemannian manifolds. This problem falls within the category of online optimization methods. We introduce the notion of geodesic dithers which is a perturbation of the optimizing trajectory in the tangent bundle of the amb...

    A Local Characterization of Lyapunov Functions and Robust Stability of Perturbed Systems on Riemannian Manifolds

    Taringoo, Farzin; Dower, Peter M.; Nešić, Dragan; Tan, Ying (2013)
    Projects: ARC | Extremum seeking control: a systematic design framework (DP120101144)
    This paper proposes several Converse Lyapunov Theorems for nonlinear dynamical systems defined on smooth connected Riemannian manifolds and characterizes properties of corresponding Lyapunov functions in a normal neighborhood of an equilibrium. We extend the methods of constructing of Lyapunov functions for ordinary differential equations on $\mathds{R}^{n}$ to dynamical systems defined on Riemannian manifolds by employing the differential geometry. By employing the derived properties of Lyap...
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