A Simultaneous Approach for Correcting Differences between Units in Multi-Unit Optimization

Multi-unit optimization is a recently proposed extremum-seeking technique where the gradient, estimated by finite difference between two identical units, is controlled to zero. The main assumption of having two identical units is rarely verified in practice and it has been noted that differences in the static characteristics can affect the stability and the equilibrium point. So, correctors have been proposed, where optimization and correction for differences are performed alternatively. This, in turn, causes a discontinuous operation leading to a hybrid dynamics. To avoid such a scenario, an approach where optimization and correction take place simultaneously, is presented. A proof of stability of the simultaneous scheme is also provided.