Extremum seeking using analog nonderivative optimizers

An extremum seeking method with continuous time nonderivative optimizers is proposed. The optimization network consists of two components: dynamic cost function unit and analog nonderivative optimizer. The presence of the dynamic cost function component, rather than a static input-output map, requires that the optimization process be separated into a two time-scale dynamics so that the extremum seeking process mimics the static function optimization process, which is inherently a two time-scale process. Separating the optimization dynamics into two time-scales allows one to use analog optimizers to solve this class of optimization problems. The two time-scale separation can be achieved in two ways. In the first approach, dynamics of the cost function unit are accelerated so that the cost function unit approximates the static map property. Then it is possible to use optimization methods suitable for static maps. The second method relies on activating the analog optimizers by opening their input channels at a certain time interval, which enforces the optimizers to run slower than the dynamic cost map unit, thereby inducing a two time-scale separation.