Extremum seeking for limit cycle minimization

In many physical problems, equilibrium stabilization is not possible and the controlled system is in a limit cycle. If the size of the limit cycle depends on some of the control parameters, then a reasonable objective would be to tune this parameter to minimize the size of the limit cycle. We propose a method for achieving this. This method is an extension of our earlier result (Kristic and Wang, 2000) on extremum seeking for equilibria. We illustrate the method with a Van der Pol oscillator example and present analysis for it using averaging and singular perturbations.