Improved performance in the multi-unit optimization method with non-identical units

In the multi-unit optimization method, the gradient is estimated using finite difference of the outputs of multiple identical units driven with inputs that are offset by a design parameter. For processes with non-identical units, it is shown that stability is not always guaranteed and that the scheme does not necessarily converge to the desired optimum. Correctors are proposed to compensate for the differences between the units. It is shown that the scheme with correctors is locally asymptotically stable and converges to the respective optimum of each units. The multi-unit optimization method with correctors is applied as an example to bioreactors producing green fluorescent protein.