Mechanical Engineering - Research Publications

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    Point-wise extremum seeking control scheme under repeatable control environment
    Tan, Y ; Mareels, I ; Nešić, D ; Xu, JX (IEEE, 2007-01-01)
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    Extremum Seeking From 1922 To 2010
    Tan, Y ; Moase, WH ; Manzie, C ; Nesic, D ; Mareels, IMY ; Chen, J (IEEE, 2010)
    Extremum seeking is a form of adaptive control where the steady-state input-output characteristic is optimized, without requiring any explicit knowledge about this input-output characteristic other than that it exists and that it has an extremum. Because extremum seeking is model free, it has proven to be both robust and effective in many different application domains. Equally being model free, there are clear limitations to what can be achieved. Perhaps paradoxically, although being model free, extremum seeking is a gradient based optimization technique. Extremum seeking relies on an appropriate exploration of the process to be optimized to provide the user with an approximate gradient, and hence the means to locate an extremum. These observations are elucidated in the paper. Using averaging and time-scale separation ideas more generally, the main behavioral characteristics of the simplest (model free) extremum seeking algorithm are established.
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    On automatic seeking of optimal steady-states in biochemical processes
    Bastin, G ; Nešić, D ; Tan, Y ; Mareels, I (IFAC, 2007-01-01)
    It is discussed how the automatic seeking of optimal steady states biochemical reactors can be achieved by using non-model based extremum-seeking control with semi-global practical stability and convergence properties. A special attention is paid to processes with multiple steady-states and multivalued cost functions.
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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 Extremum Seeking in Bioprocesses with Multivalued Cost Functions
    Bastin, G ; Nesic, D ; Tan, Y ; Mareels, I (WILEY, 2009)
    Finding optimal operating modes for bioprocesses has been, for a long time, a relevant issue in bioengineering. The problem is of special interest when it implies the simultaneous optimization of competing objectives. In this paper, we address the problem of finding optimal steady states that achieve the best tradeoff between yield and productivity by using nonmodel-based extremum-seeking control with semiglobal practical stability and convergence properties. A special attention is paid to processes with multiple steady states and multivalued cost functions.
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    On global extremum seeking in the presence of local extrema
    Tan, Y ; Nesic, D ; Mareels, IMY ; Astolfi, A (PERGAMON-ELSEVIER SCIENCE LTD, 2009-01-01)
    We propose a global extremum seeking scheme which can seek the global optimal value in the presence of local extrema. It is shown that the proposed global extremum seeking scheme can converge to an arbitrarily small neighborhood of the global extremum from an arbitrarily large set of initial conditions if sufficient conditions are satisfied. A simple example illustrates the effectiveness of the proposed scheme.
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    On the choice of dither in extremum seeking systems: A case study
    Tan, Y ; Nesic, D ; Mareels, I (PERGAMON-ELSEVIER SCIENCE LTD, 2008-05-01)
    We discuss how the choice of dither (excitation signal) affects 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.