An Adaptive Extremum Seeking Scheme for Non-Convex Optimisation

The paper presents an extremum-seeking scheme in which the dither is adaptively tuned to deal with non-convex cost functions. The adaptation law decreases the dither when local cost function trends are easily visible from output data. Contrarily, when the cost function does not have a dominant trend, the dither is increased to enrich the output data. This adaptive scheme can give advantages in practical applications when a conservatively large dither implies unnecessary high energy to optimise a cost function corrupted by non-uniform state-dependent disturbances. Numerical comparisons confirm the superior performance of the proposed solution.