The
following work presents a reformulation of the modifier-adaptation
methodology for real-time optimization as a nested optimization problem.
Using the idea of iteration over the modifiers, this method makes
it possible to find a point that satisfies the necessary conditions
of optimality (NCO) of the process, despite modeling mismatch, using
an outer optimization layer that updates the gradient modifiers with
the objective of minimizing the Lagrangian function estimation of
the process. Moreover, if a direct search algorithm is implemented
in this layer, we can find the optimum without explicitly computing
the gradients of the process. The presented scheme was tested in three
optimization examples, assuming the absence and presence of process
noise, with parametric and structural uncertainty. The results show
that in all the cases studied, the method converges to a close neighborhood
of a point that satisfies the NCO of the real plant, being robust
under noisy scenarios and without the need to estimate process derivatives.
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