Nonlinear Optimization based frameworks for Model Predictive Control, State-Estimation, Sensitivity Analysis, and Ill-posed Problems
Creators: name: Thierry, David Molina
Publisher: name: Carnegie Mellon University
Year: 2020
Subjects: subject: 90499 Chemical Engineering not elsewhere classified
subject: FOS: Chemical engineering
subject: FOS: Chemical engineering

description: The development of robust and efficient algorithms for nonlinear optimization is an important matter; because they make possible the solution of models with increasingly size<br>and complexity. In this context, the Interior Point Optimizer (IPOPT) has been proven to be a competitive algorithm, because of its ability to handle large scale problems. However, there are some specific situations in which convergence can not be guaranteed. For instance<br>the violation of a regularity condition given by the Linear Independence Constraint Qualification (LICQ). This property is given in terms of the consistency of local linearizations<br>of the set of constraints, i.e. the gradients. If the set of gradients of equality and active bound inequality are linearly independent, then the LICQ holds. It turns out that if this<br>property is not satisfied, IPOPT would attempt to regularize the system by perturbing it, with the hope to overcome regions of local inconsistency. However, if the LICQ does not<br>hold globally or if the system has severe ill-conditioned, the regularization strategies will fail. Thus, we present the `1-exact penalty-barrier strategy to deal with this lack of regularity. This works by penalizing the infeasibility with a parameter at the objective; and then by reformulating the problem to obtain a higher dimensional problem, the LICQ property holds at all points for which the new variables are nonzero. Thus achieving higher level of robustness as opposed to the regular IPOPT. Moreover, an unified framework for nonlinear model-based state-estimation and control with parametric sensitivity is presented. Typically, control strategy of a processes is tied to the ability to accommodate online computations; in this sense nonlinear optimization strategies like Moving Horizon Estimation (MHE) and Model Predictive Control (NMPC) are overlooked. Nevertheless, it has been proposed to use the parametric nature of these optimization problems to create a scheme in which the bulk of computations is partitioned into a background phase with all the most computationally expensive steps, and an online phase, in which the sensitivity information is used to make inexpensive calculations for the state estimate or controller input. These ideas have been put together into a Python framework, that streamlines the creation of a state-estimation and control strategy with the additional benefit of having parametric sensitivity embedded into it. This framework works by using the Pyomo libraries to create optimization objects and automatically discretize the models given by the user. We demonstrate the effectiveness of the framework<br>in two problems of vastly different complexity. A benchmark distillation case study and a Bubbling Fluidized Bed Reactor (BFB) for the capture of CO<sub>2</sub>. The results show that<br>sensitivity is effective for online implementations of the controller and it was seamlessly enabled by our framework.