Improved Directional Derivatives for Modifier-Adaptation Schemes

The modifier-adaptation methodology enables real-time optimization (RTO) of plant operation in the presence of considerable plant-model mismatch. It requires the estimation of plant gradients. Obtaining these gradients is expensive as it involves potentially many online experiments. Recently, a directional modifier-adaptation approach has been proposed. It relies on process models to find a subset of input directions that are critical for plant optimization in an offline computation. In turn, this allows estimating directional derivatives only in the critical directions instead of full gradients, thereby reducing the burden of gradient estimation. However, in certain cases (change of active constraints, large parametric uncertainty) directional modifier adaptation may lead to significant suboptimality. Here, we propose an extension of directional modifier adaptation, whereby we compute, at each RTO iteration, a potentially varying set of critical directions that are robust to large parametric perturbations. We draw upon a simulation study on the run-to-run optimization of the Williams-Otto semi-batch reactor to show that the proposed extension allows achieving a good trade-off between the number of critical directions and plant optimality.