Nonlinear Model Predictive Control

Promoting fundamental research and applications through the NMPC workshop

In the third year of the DAAD project “University Cooperation with the African Institutes for Mathematical Sciences (AIMS) II – Systems Optimization for Sustainable Resources Utilization”, Prof. Pu Li (Process Optimization Group of Technische Universität Ilmenau) in cooperation with the German Chair at AIMS Rwanda Dr. rer. nat. habil. Abebe Geletu organized the workshop “Nonlinear Model Predictive Control (NMPC)”, which took place in Ilmenau from 27 to 29 May 2024.

The scholarship holders are on a research stay for the summer semester at the TU Ilmenau. Here they work on their research, attend lectures, and make exchanges in their research field. Therefore, aim of the workshop is to promote theoretical studies on model-based control and optimization. It started with an introductory session, followed by three days of presentations on NMPC. Guest speakers were invited from the Department of Mathematics including Prof. Worthmann, an MPC specialist, whose lecture dealt with the theoretical foundations of NMPC. From the same department, Dr. Schmitz spoke on „Data-Driven MPC“ and Dr. Lanza on „MPC for Output Tracking with Time-Varying Output Constraints“. Prof. Li talked about the “Numerical Implementation of NMPC” and Dr. Geletu about “Stochastic NMPC”. All the lectures are essential topics for the research of the scholarship holders.

In addition to the scholarship holders from Rwanda, there were 15 other participants from different institutes of the TU Ilmenau. This gave the scholarship holders a unique opportunity to exchange ideas with other researchers from different fields. In addition to the lectures and discussions, the participants of the workshop went on an excursion to Fraunhofer IOSB-AST. They visited the laboratories of „Cognitive Energy Systems“, „Intelligent Embedded Systems“ and „Underwater Robotics“ and learned about the practical application of theoretical methods.

Schedule

Visit of the Fraunhofer IOSB-AST (Tuesday afternoon, 28.05.2024)

Stochastic Model Predictive Control: Theory, Methods and Applications (Wednesday, 29.05.2024)

Course Description:

This course introduces Stochastic Model Predictive Control (SMPC) for systems under uncertainty. It begins with an overview of uncertainties in real-world applications and probability theory, then covers characterization of uncertainties to determine appropriate optimization models and control strategies. Standard model-based control strategies are briefly discussed. Key topics include initial state selection, recursive feasibility, and stability issues of MPC for linear and nonlinear stochastic systems, with a focus on chance-constrained approaches. The course also briefly covers numerical methods, real-world applications, and advanced topics in current SMPC research and developments.

Course Content:

1. Uncertainties in Applications
2. Uncertainties and Probability: A brief review
3. Optimization and Control under Uncertainty
4. Model Predictive Control (MPC)
   1. Linear Stochastic Systems
   2. Nonlinear Stochastic Systems
5. Solution Methods for Chance Constrained Stochastic MPC
6. Applications
7. Advanced topics