Fast extremum-seeking on Hammerstein plants

The prevailing analyses of sinusoidally perturbed extremum-seeking (ES) schemes require the ES scheme to act slowly relative to the plant dynamics. Existing analyses that do allow for fast ES are fairly restrictive, considering only local behaviour on Wiener-Hammerstein plants where the nonlinear element is quadratic. In this paper, semi-global stability of an ES scheme acting on a general Hammerstein plant is considered. A simple tuning approach is presented, allowing the ES scheme to achieve arbitrarily fast convergence of the plant input from an arbitrarily large set of initial conditions to an arbitrarily small neighbourhood of the value that minimises (or maximises) the plant output.