Extremum-seeking control for nonlinear systems with periodic steady-state outputs

Extremum-seeking control is a powerful adaptive technique to optimize system performance. To this date, extremum-seeking control has mainly been used to optimize plants with constant steady-state outputs, whereas the non-equilibrium case, in which the steady-state outputs are time varying, has received relatively little attention compared to the equilibrium case. In this paper, we propose an extremum-seeking scheme for the optimization of nonlinear plants with periodic steady-state outputs. Extremum-seeking control in this non-equilibrium setting is relevant in, for example, the scope of tracking and disturbance rejection problems. Using the concept of semi-global practical asymptotic stability, 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.