A class of adaptive feedforward control using multiplexed extremum seeking

Most extremum seeking design approaches consider optimising the steady state output of a plant with stationary input-output behaviour. However, when the plant is subject to a time-varying exogenous disturbance, the plant extremum point may vary accordingly. This paper firstly considers the effect of slowly varying exogenous inputs on the performance of a black-box extremum seeking scheme. The analysis reveals that, under proper tuning, the extremum seeking controller converges to the extremum of an average map. A multiplexed extremum seeking framework that estimates the mapping between the extremum point and the disturbance signal is then proposed. The approach is demonstrated via simulation to achieve a finer estimation of the extremum map.