A Perturbation-Based Proportional Integral Extremum-Seeking Control Approach

This paper proposes a proportional-integral extremum-seeking control technique. The technique is a generalization of the standard perturbation based techniques which provides fast transient performance of the closed-loop system to the optimum equilibrium of a measured cost function. Under the assumption that the equations describing the dynamics of the nonlinear system and the cost function to be minimized are unknown, it is shown that, for a class of minimum-phase nonlinear system with a cost function of relative degree one, the closed-loop ESC can practically stabilize the unknown equilibrium optimum. The stabilization result provides an alternative approach to output feedback control of nonlinear systems.The effectiveness of the proposed approach is demonstrated using simulation examples.

[1]  Denis Dochain,et al.  Adaptive extremum seeking control of continuous stirred tank bioreactors with unknown growth kinetics , 2004, Autom..

[2]  Miroslav Krstic,et al.  Performance improvement and limitations in extremum seeking control , 2000 .

[3]  Kartik B. Ariyur,et al.  Real-Time Optimization by Extremum-Seeking Control , 2003 .

[4]  Miroslav Krstic,et al.  Extremum seeking for moderately unstable systems and for autonomous vehicle target tracking without position measurements , 2006 .

[5]  Martin Guay,et al.  Parameter convergence in adaptive extremum-seeking control , 2007, Autom..

[6]  Tankut Acarman,et al.  Stability and performance improvement of extremum seeking control with sliding mode , 2003 .

[7]  Chris Manzie,et al.  A systematic approach to extremum seeking based on parameter estimation , 2010, 49th IEEE Conference on Decision and Control (CDC).

[8]  Chunlei Zhang,et al.  Extremum-Seeking Control and Applications: A Numerical Optimization-Based Approach , 2011 .

[9]  Miroslav Krstic,et al.  Multivariable Newton-based extremum seeking , 2011, IEEE Conference on Decision and Control and European Control Conference.

[10]  John Tsinias,et al.  Averaging Criteria for Asymptotic Stability of Time-Varying Systems , 2014, IEEE Transactions on Automatic Control.

[11]  Ying Tan,et al.  On non-local stability properties of extremum seeking control , 2006, Autom..

[12]  Kevin Barraclough,et al.  I and i , 2001, BMJ : British Medical Journal.

[13]  Martin Guay,et al.  A comparison of extremum seeking algorithms applied to vapor compression system optimization , 2014, 2014 American Control Conference.

[14]  Ying Tan,et al.  A non-gradient approach to global extremum seeking: An adaptation of the Shubert algorithm , 2013, Autom..

[15]  Chunlei Zhang,et al.  Robust and adaptive design of numerical optimization-based extremum seeking control , 2009, Autom..

[16]  A. Teel,et al.  Solving smooth and nonsmooth multivariable extremum seeking problems by the methods of nonlinear programming , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[17]  Miroslav Krstic,et al.  Minimum-Seeking for CLFs: Universal Semiglobally Stabilizing Feedback Under Unknown Control Directions , 2013, IEEE Transactions on Automatic Control.

[18]  A. Teel,et al.  Semi-global practical asymptotic stability and averaging , 1999 .

[19]  I. Mareels,et al.  Extremum seeking from 1922 to 2010 , 2010, Proceedings of the 29th Chinese Control Conference.

[20]  Milos S. Stankovic,et al.  Lie bracket approximation of extremum seeking systems , 2011, Autom..

[21]  Miroslav Krstic,et al.  Stability of extremum seeking feedback for general nonlinear dynamic systems , 2000, Autom..

[22]  Hans-Bernd Dürr,et al.  Saddle Point Seeking for Convex Optimization Problems , 2013, NOLCOS.

[23]  Ümit Özgüner,et al.  Extremum seeking with sliding mode gradient estimation and asymptotic regulation for a class of nonlinear systems , 2011, Autom..

[24]  M. Guay,et al.  ADAPTIVE EXTREMUM SEEKING CONTROL OF NONLINEAR DYNAMIC SYSTEMS WITH PARAMETRIC UNCERTAINTIES , 2002 .

[25]  Chris Manzie,et al.  Newton-Like Extremum-Seeking for the Control of Thermoacoustic Instability , 2010, IEEE Transactions on Automatic Control.

[26]  Miroslav Krstic,et al.  Optimizing bioreactors by extremum seeking , 1999 .

[27]  Chris Manzie,et al.  Fast extremum-seeking for Wiener-Hammerstein plants , 2012, at - Automatisierungstechnik.

[28]  Denis Dochain,et al.  A proportional-integral extremum-seeking controller design technique , 2017, Autom..

[29]  Jin Soo Lee,et al.  Extremum seeking control for discrete-time systems , 2002, IEEE Trans. Autom. Control..