Extremum-seeking control for periodic steady-state response optimization

Extremum-seeking control is a powerful adaptive technique to optimize steady-state system performance. To this date, extremum-seeking control has mainly been used to optimize plants with constant steady-state outputs, whereas the case in which the steady-state outputs are time varying, has received less attention. We propose an extremum-seeking scheme for the optimization of nonlinear plants with periodic steady-state outputs. Extremum-seeking control in this setting is relevant in e.g. the scope of tracking and disturbance rejection problems. We show that under certain assumptions the proposed extremum-seeking controller design guarantees that for an arbitrarily large set of initial conditions the steady-state performance of the plant converges arbitrarily close to its optimal value.