(101a) Deterministic Global Dynamic Optimization of Hammerstein-Wiener Models

Hammerstein-Wiener (HW) models represent a significant class of data-driven models. They are block-structured models that consist of two static nonlinear blocks preceding and following a linear block with the system’s dynamics. Over the past years, numerous studies on identification of these systems have been reported in the literature, cf., e.g., [1-4]. HW models have been employed to model a wide spectrum of physical, chemical, and biological systems [5]. Especially in chemical engineering, they have been often used for process modeling and control, cf., e.g., [4,5].

The overall structure of HW models is inherently nonlinear, and thus optimization problems with these models embedded may exhibit suboptimal local minima. Local approaches are common practice in solving dynamic optimization problems, mainly due to their computational advantages. However, global optimization can be crucial for determining process validity (cf., e.g., parameter estimation studies [6, 7]) and can have a profound effect on process profitability [8]. Over the past few years, significant developments on global dynamic optimization have been accomplished [9]. Yet, research in this field lies still on an initial stage.

In this work, we present a novel computational algorithm to solve HW models to global optimality. More precisely, we expand recent theory for global optimization of systems with linear ODEs embedded [10] to HW models. In particular, we introduce additional optimization variables beside the degrees of freedom to enable the application of the theory of Singer and Barton [10]. For the numerical solution of the problem we apply a discretize-then-relax method to obtain a nonlinear program (NLP), which we formulate in a reduced-space fashion similar to [11]. The NLPs are solved with our open-source global optimization software MAiNGO [12]. MAiNGO is based on McCormick relaxations [13] and subgradient propagation as presented in [14]. We test our optimization strategy for different numerical case studies, both for off-line and on-line (nonlinear model predictive control) applications.

The results demonstrate the potential benefits of the presented approach over a wide field of applications. Computational effort of our approach scales favorably with refining state discretization, but is in general more sensitive to the number of control parameters. Therefore, our approach is particularly promising in the control field, where problems with short time horizons and few control elements are solved iteratively.

Acknowledgements:
The authors gratefully acknowledge the financial support of the Kopernikus project SynErgie by the Federal Ministry of Education and Research (BMBF) and the project supervision by the project management organization Projektträger Jülich. The authors would like to thank Adel Mhamdi for fruitful discussions and recommendations throughout the development of this work.

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