Real-Time Optimization via Modifier Adaptation

In the presence of uncertainty, the necessary conditions of optimality (NCO) predicted by the model do not match those of the plant. This implies that model-based optimal inputs, though optimal for the model, are unlikely to be optimal for the plant, leading to infeasibility and/or suboptimal performance. Originally developed for static optimization problems, RTO via modifier adaptation uses plant measurements and re-optimization to iteratively modify the NCO predictions. The nominal plant model is kept unchanged, while zeroth-order correction terms are added to the modeled constraints (to correct the predicted value of the constraints), and input-affine correction terms are added to both the cost and the constraints (to correct the predicted values of the gradients).

 

The nicest feature of the modifier-adaptation scheme is that, upon convergence, the NCO of the modified optimization problem match the plant NCO, and thus the resulting inputs are guaranteed to be a local extremum for the plant, even in the presence of plant-model mismatch. The ability to estimate the cost and constraint gradients for the plant is key to the success of modifier-adaptation schemes as these elements are required for constructing the input-affine correction terms.