Extension of the global optimization using multi-unit extremum seeking control for noisy scalar systems

An efficient global optimization method based on multi-unit extremum seeking has been proposed recently for noise-free nonlinear continuous static, scalar systems. Herein, a monotonically decreasing offset is introduced between the inputs of two identical units and the estimated gradient by finite difference is controlled to zero by an integrator. This paper is the extension of the mentioned algorithm to globally optimize scalar objective functions with the presence of noise. The algorithm is applied on several noisy global optimization test problems to show the capability of this methodology.