Correction for Non-identical Units in Multi-unit Optimization ⋆

Extremum-seeking control is a class of methods where real-time static optimization of a dynamic system is achieved by controlling the gradient. Estimation of the gradient is a key issue in extremum-seeking methods. In multi-unit optimization, the gradient is obtained using finite difference of the outputs of multiple identical units driven with inputs that are offset by a design parameter. However, if the units are not identical, the stability of such a scheme is in question and the point where the scheme converges could be far from the desired optimum. This paper proposes correctors to compensate for the differences between the units. It is shown that the scheme with correctors is locally asymptotically stable and converges to the desired optimum for all the units. The multi-unit optimization method with correctors is applied to bioreactors producing green fluorescent protein.