Electrical and Electronic Engineering - Research Publications

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Start date: 2006 × End date: 2006 × Author: Nesic, Dragan × Author: Mareels, Iven ×

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    On global extremum seeking in the presence of local extrema
    Tan, Y ; Nesic, D ; Mareels, I ; Astolfi, A (IEEE, 2006-01-01)
    We analyze global extremum seeking in the presence of local extrema for static nonlinear maps controlled by a scalar extremum seeking scheme that was recently proposed in [1]. Sufficient conditions are given under which it is possible to tune the controller parameters to achieve convergence to an arbitrarily small neighborhood of the global extremum in the presence of local extrema from an arbitrarily large set of initial conditions. Several examples provide insights and highlight the potential difficulties that one would face when trying to generalize our results.
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    On the choice of dither in extremum seeking systems: A case study
    Nesic, D ; Tan, Y ; Mareels, I (IEEE, 2006-01-01)
    We discuss how the dither (excitation signal) shape affects on the performance of extremum seeking using a benchmark situation: a static scalar map; and a simple scalar extremum seeking scheme. Our comparisons are based on the performance of the system with different dithers in terms of three performance indicators: the speed of convergence, domain of attraction and accuracy (i.e. the ultimate bound on trajectories). Our analysis explicitly shows how the dither shape affects each of these performance indicators. Our study suggests that the practitioners using extremum seeking control should consider the dither shape as an important design parameter. Computer simulations support our theoretical findings.
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    On non-local stability properties of extrernum seeking control
    Tan, Y ; Nesic, D ; Mareels, I (PERGAMON-ELSEVIER SCIENCE LTD, 2006-06-01)
    In this paper, we consider several extremum seeking schemes and show under appropriate conditions that these schemes achieve extremum seeking from an arbitrarily large domain of initial conditions if the parameters in the controller are appropriately adjusted. This non-local stability result is proved by showing semi-global practical stability of the closed-loop system with respect to the design parameters. We show that reducing the size of the parameters typically slows down the convergence rate of the extremum seeking controllers and enlarges the domain of the attraction. Our results provide guidelines on how to tune the controller parameters in order to achieve extremum seeking. Simulation examples illustrate our results.