Static optimization via tracking of the necessary conditions of optimality using neighboring extremals

In the framework of process optimization, the use of measurements to compensate the effect of uncertainty has reemerged as an active area of research. One of the ideas therein is to directly track the necessary conditions of optimality (NCO tracking). NCO tracking for steady-state optimization consists of monitoring the active constraints and pushing certain sensitivities to zero. In standard extremum-seeking controllers, the sensitivities are evaluated by perturbation of the inputs, which can be experimentally expensive. Fortunately, more measurements (typically the outputs) than just the cost function are available. The idea is to incorporate the output measurements in the optimization framework for estimating the sensitivities, and thereby implementing the update laws. It is shown that this approach can bring the system fairly close to the optimum with relatively few experimental trials.