Mechanical Engineering - Research Publications

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Author: Dower, Peter × Author: Nesic, Dragan × Start date: 2014 ×

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    Extremum seeking control for nonlinear systems on compact Riemannian manifolds
    Taringoo, F ; Nesic, D ; Tan, Y ; DOWER, PM (IEEE Press, 2014)
    This paper formulates the extremum seeking control problem for nonlinear dynamical systems which evolve on Riemannian manifolds and presents stability results for a class of numerical algorithms defined in this context. The results are obtained based upon an extension of extremum seeking algorithms in Euclidean spaces and a generalization of Lyapunov stability theory for dynamical systems defined on Rimannian manifolds. We employ local properties of Lyapunov functions to extend the singular perturbation analysis on Riemannian manifolds. Consequently, the results of the singular perturbation on manifolds are used to obtain the convergence of extremum seeking algorithms for dynamical systems on Riemannian manifolds.
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    Coordination of blind agents on Lie groups
    Taringoo, F ; Nesic, D ; DOWER, P ; Tan, Y (IEEE, 2015)
    This paper presents an algorithm for the synchronization of blind agents evolving on a connected Lie group. We employ the method of extremum seeking control for nonlinear dynamical systems defined on connected Riemannian manifolds to achieve the synchronization among the agents. This approach is independent of the underlying graph of the system and each agent updates its position on the connected Lie group by only receiving the synchronization cost function.
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    Optimization Methods on Riemannian Manifolds via Extremum Seeking Algorithms
    Taringoo, F ; Dower, PM ; Nesic, D ; Tan, Y ( 2014-12-09)
    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 ambient state manifolds and obtain the extremum seeking closed loop as a perturbation of the averaged gradient system. The main results are obtained by applying closeness of solutions and averaging theory on Riemannian manifolds. The main results are further extended for optimization on Lie groups. Numerical examples on Riemannian manifolds (Lie groups) SOp3q and SEp3q are also presented at the end of the paper.
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    Optimization Methods on Riemannian Manifolds via Extremum Seeking Algorithms
    TARINGOO, F ; Dower, PM ; Nesic, D ; Tan, Y (Society for Industrial and Applied Mathematics, 2018)
    This paper formulates the problem of extremum seeking for optimization of cost function 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 ambient state manifolds, and obtain the extremum seeking closed loop as a perturbation of the averaged gradient system. The main results are obtained by applying closeness of solutions and averaging theory on Riemannian manifolds. The main results are further extended for optimization on Lie groups. Numerical examples on the Stiefel manifold V3;2 and the Lie group SEp3q are presented at the end of the paper.