## 2022 - 2024

Analysis and Control of Nonlinear Hyperbolic Systems with Degeneration on Networks

## 2021 - now

**BaCaTeC. **Data-Based Optimization in Real Time for Dynamic Systems

## 2021 - now

**sherpa.ai** Technological transfer

## 2018 - now

**SFB Transregio TRR154. **Mathematical modelling, simulation and optimization using the example of gas networks

## 2018 - now

**e-Learning.** Calculus and Basic stats with R / Math for Engineers

## 2017 - 2019

DFG-Priority Programme **SPP 1679**

## 2019 - now

**FAU DCN-AvH.**Chair for Dynamics, Control and Numerics - Alexander von Humboldt Professorship

Modeling, Robust Design and Control of Gas Networks (2022 – )

Simulation and Optimization on Finite Graphs is considered for the example of Gas Networks. We are interested in two models defined on the graph. The first model for steady state solutions. The second model for evolution problems. The steady state solutions are considered for the geometrical optimization and robust design of the structure.

Modellierung, Analysis und Steuerung degenerierter nichtlinearer hyperbolischer Systeme auf Netzwerken (2022 – 2024)

DFG WA5144/1-1

This project focusses on control problems for elastic bodies arising in particular in structural mechanics, e.g. flexible multi-link structures, pipe-systems, string-mass-spring-systems or highly flexible robots, where degeneration (damage and failure) takes place at the boundaries or in multiple joints. The long-time goal is to develop control strategies that guarantee optimal performance while also respect the life-cycle of the structures. This project is supported by DFG Individual Research Grant.

(welcome applications for the research internship positions in a form of Master thesis) 2022 – 2024

Emerging Talents Initiative (ETI) No.5500168

In recent years, Physics-Informed Neural Networks (PINNs) have started to arise frequently in many areas of science and engineering. PINNs are revolutionizing the way many physics-related problems are solved by combining classic Neural Networks explicitly with the underlying Physics of a certain problem. This is a collaboration with Fraunhofer IISB, Erlangen. The research here is supported by the Emerging Talents Initiative (ETI).

HighTech Research between Bavaria and California (2021 – now)

Unlike most machine learning algorithms, which have yet to be equipped with guarantees of convergence and stability in real time for feedback applications to dynamical systems, one of the earliest example of data-based optimization algorithms, the so-called “extremum seeking” (ES) approach, whose original idea is traced back to a century-old patent in France in 1922, possesses provable properties of stability and even assignable convergence rates. This an example of Artificial Intelligence (AI) decades before the notion of AI was formalized. For finite-dimensional systems, the mathematical guarantees for ES were developed by Prof. M. Krstic around 2000. Over the last few years, he has extended the ES algorithm design and stability analysis from Ordinary Differential Equations (ODE) to Partial Differential Equations (PDE). The visit by Prof. M. Krstic to FAU will be an opportunity to explore the cooperation in this area with further PDE applications in view, including gas transport networks.

### Technological transfer

June 2021 – now

Recommendation Systems and Machine Learning

Mathematical Modelling, Simulation and Optimization using the example of Gas Networks (2018 – now)

Subprojects where our team are members are working at:

Dynamic simulation of interconnected solids processes. (2017 – 2019)

The material and the energy conversion of technical processes often consist of many individual substeps, which are interconnected by material, energy and information flows. The networking of each component has significant influence on the dynamic behavior and the stability of such processes. For the design and optimization, especially with respect to the reduction of energy and raw material demands, not only the individual components should be simulated, but also the dynamic behavior of the total process. This is state of the art in fluid process engineering as there are several tools commercially available for dynamic flowsheet simulation. However, such tools and dynamic models, that allow for a dynamical flowsheet simulation independent of the considered system, are missing for the field of solids process engineering. The reason for this is the complex description of solids with their multivariate disperse parameters and the associated processes for the conversion of solids. The main focus of the Priority Programme is the development of numerical tools of the dynamic simulation of interconnected solids process. Therefore, the dynamic models of each machine and apparatuses of solids process engineering should be formulated and implemented.

Higher Education. Internationalisation 2.0. Calculus and Basic Stats with R and Math for Engineers (now)

Higher Education. Internationalisation 2.0. Calculus and Basic Stats with R (2018-now). Transition Studies are being developed at FAU to help foreign students enter the Master’s program at FAU. Mathematics is involved in this project and is developing the online courses Calculus and Basic Stats with R.

MathInEE. Math for Engineers: Starting Sucessfully. In the context of this project, Nicolai von Schroeders (Mathematics Didactics) and Wigand Rathmann are developing a new concept for the Mathematics Repetitorium of the Faculty of Technology. The redesign means adapting the content to the changed conditions and the material will be reprocessed accordingly from a didactic point of view.

Chair for Dynamics, Control and Numerics – Alexander von Humboldt Professorship (2019 – now)

Funded by Alexander von Humboldt Stiftung/Foundation, the Chair for Dynamics, Control and Numerics – Alexander von Humboldt Professorship reach its activities a step further with a wide expertise in the areas of Applied Mathematics, PDE analysis, control theory, numerical analysis and computational mathematics.