Extremum seeking for limit cycle minimization

In many physical problems equilibrium stabilization is not possible and the controlled system is in a limit cycle (of a possibly reduced size). 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. In this paper we propose a method for achieving this. This method is an extension of our earlier result (CDC 1997) on extremum seeking for equilibria. We illustrate the method with a Van der Pol oscillator example and present analysis using averaging and singular perturbations.