A Shahshahani Gradient based extremum seeking scheme

We present a novel scheme of a deterministic continuous extremum seeking control based on evolutionary game theory (EGT), which allows the optimization in real-time of non-modeled multivariable dynamic systems under inequality and equality constraints. Unlike traditional extremum seeking controllers, which use classical Euclidean gradient-based optimization methods, the scheme proposed is based on the Shahshahani Gradient, which emerges in some evolutionary games. The notion of maximal in the plant and its stability properties are correlated with the concepts of Nash equilibrium and evolutionarily stable states (ESS). The implementation of the algorithm is illustrated via simulation.