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 the theory for convergence to 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 the improved computational performance of the proposed solution approach over alternative options not exploiting the linear dynamics discussed in the manuscript, and underline the high potential of our method especially when used for online applications like nonlinear model predictive control.
Process Systems Engineering (AVT.SVT), RWTH Aachen University, 52074 Aachen, Germany, June 2020