CONVERGENCE OF MULTI-UNIT OPTIMIZATION WITH NON-IDENTICAL UNITS: APPLICATION TO THE OPTIMIZATION OF A BIOREACTOR

Abstract

Multi-unit optimization is a new extremum seeking method (real-time steady state optimization of a dynamic system by controlling the gradient), where the gradient is obtained using finite difference of the outputs of multiple identical units driven with inputs that differ by a design parameter Δ. A major limitation of this approach is that the convergence is established only when units are identical. This paper addresses the convergence of the multi-unit scheme with non-identical units. With a simple quadratic approximation of the objective function, it is shown that the scheme converges only when the Δ is either larger than or in a direction opposite to that of the difference between their optimum values. The optimal choice of Δ is addressed. The theoretical ideas are illustrated on the optimization of a bioreactor producing green fluorescent protein.