Global dynamic optimization with Hammerstein–Wiener models embedded

Journal of Global Optimization, vol. 84, pp. 321–347

Abstract

Abstract Hammerstein–Wiener models constitute a significant class of block-structured dynamic models, as they approximate process nonlinearities on the basis of input–output data without requiring identification of a full nonlinear process model. Optimization problems with Hammerstein–Wiener models embedded are nonconvex, and thus local optimization methods may obtain suboptimal solutions. In this work, we develop a deterministic global optimization strategy that exploits the specific structure of Hammerstein–Wiener models to extend existing theory on global optimization of systems with linear dynamics. At first, we discuss alternative formulations of the dynamic optimization problem with Hammerstein–Wiener models embedded, demonstrating that careful selection of the optimization variables of the problem can offer significant numerical advantages to the solution approach. Then, we develop convex relaxations for the proposed optimization problem and discuss implementation aspects to obtain the global solution focusing on a control parametrization technique. Finally, we apply our optimization strategy to case studies comprising both offline and online dynamic optimization problems. The results confirm an improved computational performance of the proposed solution approach over alternative options not exploiting the linear dynamics for all considered examples. They also underline the tractability of deterministic global dynamic optimization when using few control intervals in online applications like nonlinear model predictive control.

Authors 5

1. Chrysoula Dimitra Kappatou Aachen Process Systems Engineering (AVT.SVT)

   RWTH Aachen University

   Affiliation as printed

   Process Systems Engineering (AVT.SVT), RWTH Aachen University, Aachen, Germany

   Process Systems Engineering (AVT.SVT), RWTH Aachen University, 52074, Aachen, Germany

2. Dominik Bongartz Aachen Process Systems Engineering (AVT.SVT)

   RWTH Aachen University

   Affiliation as printed

   Process Systems Engineering (AVT.SVT), RWTH Aachen University, Aachen, Germany

   Process Systems Engineering (AVT.SVT), RWTH Aachen University, 52074, Aachen, Germany

3. Jaromił Najman Aachen Process Systems Engineering (AVT.SVT)

   RWTH Aachen University

   Affiliation as printed

   Process Systems Engineering (AVT.SVT), RWTH Aachen University, Aachen, Germany

   Process Systems Engineering (AVT.SVT), RWTH Aachen University, 52074, Aachen, Germany

4. Susanne Saß Aachen Process Systems Engineering (AVT.SVT)

   RWTH Aachen University

   Affiliation as printed

   Process Systems Engineering (AVT.SVT), RWTH Aachen University, Aachen, Germany

   Process Systems Engineering (AVT.SVT), RWTH Aachen University, 52074, Aachen, Germany

5. Alexander Mitsos corresponding Aachen Process Systems Engineering (AVT.SVT)

   Forschungszentrum Jülich · RWTH Aachen University

   Affiliation as printed

   Institute of Energy and Climate Research: Energy Systems Engineering (IEK-10), Forschungszentrum Jülich GmbH, Jülich, Germany

   JARA-CSD, Aachen, Germany

   Process Systems Engineering (AVT.SVT), RWTH Aachen University, Aachen, Germany

   Process Systems Engineering (AVT.SVT), RWTH Aachen University, 52074, Aachen, Germany