Prof. Dr. Enrique Zuazua. Friedrich-Alexander-University of Erlangen-Nuremberg. Department of Data Science
Prof. Dr. Miroslav Krstic. University of California, San Diego. Department of Mechanical and Aerospace Engineering

Data-Based Optimization in Real Time for Dynamic Systems. BaCaTeC – HighTech Research between Bavaria and California.

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.

TRR154. Mathematical Modelling, Simulation and Optimization using the example of Gas Networks

Enrique Zuazua, Martin Gugat, Michael Schuster and Lukas Wolff from our team are members of the TRR154 – SFB Transregio 154 at the subprojects:

  • C03: Nodal control and the turnpike phenomenon
  • C05: Observer-based data assimilation for time dependent flows on gas networks
  • C08: Random Batch Methods for Optimal Control of Network Dynamics (2018-2021)
  • Uncertainty (2018-2021)

TRR154 | C03.
Nodal control and the turnpike phenomenon

Turnpike results provide connections between the solutions of transient and the corresponding stationary optimal control problems that are often used as models in the control of gas transport networks. In this way turnpike results give a theoretical foundation for the approximation of transient optimal controls by the solutions of stationary optimalcontrol problems that have a simpler structure. Turnpike studies canalso be considered as investigations of the structure of the transient optimal controls. In the best case the stationary optimal controls approximate the transient optimal controls exponentially fast.

TRR154 | C05. Observer-based data assimilation for time dependent flows on gasnetworks

This project studies data assimilation methods for models of compressible flows in gas networks. The basic idea of data assimilation is to include measurement data into simulations during runtime in order to make their results more precise and more reliable. This can be achieved by augmenting the original model equations with control terms at nodes and on pipes that steer the solutions towards the measured data. This gives rise to a new system called “observer”. This project is going to explore how much data is needed so that convergence of the observer towards the solution of the original system can be guaranteed, how fast this convergence is and how measurement errors affect the solution.

e-Learning

Internationalisation 2.0. Calculus and Basic Stats with R

Math for Engineers: Starting Sucessfully


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Chair for Dynamics, Control and Numerics – Alexander von Humboldt Professorship

Funded by Alexander von Humboldt Stiftung/Foundation, the Chair for Dynamics, Control and Numerics – Alexander von Humboldt Professorship reach its activities a step further

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