Real-time Global Optimization using Multiple Units

Abstract

Extremum-seeking schemes are real-time optimization methods that control the gradient to zero. Most of these methods can converge only to the closest local optimum, though recently, some schemes have been proposed for global optimization of a restrictive class of nonlinear maps. In this paper, the multi-unit optimization framework is used, where an offset is introduced between the inputs of two identical units and the gradient is estimated by finite difference. It is shown that if the offset is reduced to zero, the system can be made to converge to the global optimum for all nonlinear continuous static, scalar maps. Several illustrative examples are presented to show the capability of this methodology.