Extremum Seeking under Input Constraint for Systems with A Time-varying Extremum

This paper studies extremum seeking under input constraint for static plants with a time-varying extremum. We design an online optimization scheme based on extremum seeking control to solve this problem. No explicit information on the model is needed except that the output is measurable to implement this method. A saturation function is used to constrain the input of the plant while an anti-windup mechanism is employed to eliminate the side effect of the saturation function. We show that the control input converges to a neighborhood of the time-varying extremum input which means that the proposed method is capable to track the time-varying extremum input and hence, the output is kept at the extremum value. Simulation is conducted to demonstrate the effectiveness of the proposed method.