On enforcing the necessary conditions of optimality under plant-model mismatch - What to measure and what to adapt?

Industrial processes are run with the aim of maximizing economic profit while simultaneously meeting process-critical constraints. To this end, model-based optimization can be performed to ensure optimal plant operations. Usually, inevitable model inaccuracies are dealt by collecting the plant measurements at the local operating conditions in order to adapt model parameters, followed by numerical re-optimization. This iterative two-step procedure often results in a sub-optimal solution, since the models are typically not designed for optimization.

Modifier Adaptation (MA) is a Real-Time Optimization (RTO) technique that directly adds the affine-correction terms to the model. The affine corrections are parametrized in modifiers that are tailored to the optimization needs. This enables modifier adaptation to guarantee, upon convergence, matching the plant and the modified model's optimality conditions. However, computing the modifiers requires estimates of the plant gradients that are obtained via expensive plant experiments. The experimental cost can be reduced by relying more on the model of the considered plant. For example, Directional Modifier Adaptation (DMA) relies on offline-computed local parametric sensitivity analysis performed on the gradient of the Lagrangian function of the model resulting in reduced number of input directions that describe the gradient uncertainty in the model. Thereby, plant gradients are estimated only in a low-dimensional space of privileged input directions considerably reducing the experimental costs. However, local sensitivity analysis is often ineffective when the gradient of the model is considerably nonlinear in parameters.

This thesis proposes an online procedure based on global sensitivity analysis for finding the most promising privileged directions that adequately compensates for the model deficiencies in predicting the plant optimality conditions. The discovered privileged directions are such that, upon parametric perturbations, the gradient varies a lot along the privileged directions and varies only a little along the remaining input directions. Consequently, the gradients of the model cost and constraints are corrected only along the privileged directions by adapting modifiers. The resulting methodology is named as Active Directional Modifier Adaptation (ADMA). Several simulation studies conducted show that the proposed approach reaches the near-optimality conditions at a considerably reduced experimental cost.

In addition, this thesis attempts to establish a direct relation between the optimality conditions and the parameters of a given model. Model parameters are analyzed to discover mirror parameters that mimic the behavior of modifiers in influencing the optimality conditions. It is proposed to adapt mirror parameters instead of modifiers yielding the benefit of both, modifier adaptation in enforcing optimality conditions and of parameter adaptation in better noise handling and convergence.

Moreover, it is investigated how to establish the synergies between privileged input directions with model parameters in order to reduce experimental efforts. The steady-state optimization of a simulated chemical process shows that the privileged directions and the selected parameters work together to reach near-optimal performance.

Finally, the study on the power maximization of flying kites leads to the development of trust-region based ADMA method to better control the input step size.