  We consider perturbation-based extremum seeking, which recovers an
approximate gradient of an analytically unknown objective function through
measurements. Using classical needle variation analysis, we are able to
explicitly quantify the recovered gradient in the scalar case. We reveal that
it corresponds to an averaged gradient of the objective function, even for very
general extremum seeking systems. From this, we create a recursion which
represents the learning dynamics along the recovered gradient. These results
give rise to the interpretation that extremum seeking actually optimizes a
function other than the original one. From this insight, a new perspective on
global optimization of functions with local extrema emerges: because the
gradient is averaged over a certain time period, local extrema might be evened
out in the learning dynamics. Moreover, a multidimensional extension of the
scalar results is given.
