Global output-feedback extremum seeking control via monitoring functions

This paper addresses the design of an extremum-seeking controller based on monitoring function for a class of single-input-single-output (SISO) uncertain nonlinear systems. We demonstrate that it is possible to achieve an arbitrarily small neighborhood of the desired optimal point using only output-feedback. The key idea is the combination of a monitoring function with a norm state observer. We show that, as an important advantage, the proposed scheme achieves the extremum of a unknown nonlinear mapping for all domain of initial conditions, i.e., the real-time optimization algorithm has global convergence/stability properties. Moreover, some tuning rules are given to achieve convergence to global maximum in the presence of local extrema. A numerical example illustrates the viability of the proposed approach.