Research

Third Party Funded Projects

Third Party Funded Projects

Ongoing third party funded projects

 

 

 

TRR 391 B02: Statistical methods for energy systems
Aggregation and decomposition

TRR 391 B02: Statistical methods for energy systems – Aggregation and decomposition

In the subproject B02 of the Collaborative Research Center/Transregio CRC/TRR 391 Spatio-temporal Statistics for the Transition of Energy and Transport, we construct and investigate statistical methods for aggregation and decomposition to tackle the complexity of energy distribution networks, which can involve easily several 100 individual items with corresponding storage dynamics, e.g. electrical vehicles, controllable loads in households, and energy storage systems. Our analysis takes the perspective of upper-level energy transmission networks towards the statistical behavior of lower-level distribution grids at the vertical grid coupling between both layers. Aggregation of the storage dynamics of energy distribution networks can improve system operation on the transmission system via temporal couplings. Control actions decided upon on the transmission level in turn need to be mapped to the individual items composing the distribution systems. In other words, it is necessary to ensure that the action computed for aggregated abstractions can be disaggregated, i.e., control actions can be assigned in a feasible manner to the individual devices.

We thus aim to construct aggregations which admit statistical guarantees (a) on the temporal evolution of aggregated non-stationary statistics at the coupling, especially with respect to energy demand and active and reactive power fluctuations, and (b) for feasible disaggregation.

The project leaders are Prof. Dr. Roland Fried @ TU Dortmund University and Prof. Dr.-Ing. Timm Faulwasser @ TUHH. Other ICS members involved in the project include Ruchuan Ou and Oleksii Molodchyk.

 

 

Project C05: Adaptive and learning-based control architectures for SMART reactors

Project C05: Adaptive and learning-based control architectures for SMART reactors

This project is part of CRC 1615: SMART Reactors for Future Process Engineering.

Using a reactor for multiple purposes as well as autonomous process operation can only be achieved through pushing automation and control to unprecedented levels of data-driven and learning-based adaptation. Moreover, feedback control allows to compensate and alleviate unforeseen disturbances and faults, i.e., control fosters resilience. Transfer between locations and scales means that also the underlying control architectures must be designed with adaptation in mind. On this canvas, project C05 considers two main research questions: How to enable multipurpose operation through process-informed learning-based control and how to reconcile sustainability and resilience through measurement-based feedback optimization? The former is approached through a hybrid modelling strategy, wherein first-principles models are combined with reaction and process specific data-driven model components. The latter is approached using safe variants of Wiener kernel regression for real-time optimization.

Principle Investigator: Prof. Dr.-Ing. Timm Faulwasser

Coworker: Dr. Srimanta Santra

 

 

Active Learning for Systems and Control (ALeSCo)
Data Informativity, Uncertainty, and Guarantees

Active Learning for Systems and Control (ALeSCo) - Data Informativity, Uncertainty, and Guarantees

In the ALeSCo Research Unit (FOR 5785) the ICS works on the following projects:

P2: Neural ODE training via stochastic control and uncertainty quantification

Principle Investigator: Prof. Dr.-Ing. Timm Faulwasser

Data-driven and learning-based approaches for modelling of dynamic systems and for design of control laws have gained prominence in recent years. Due to their universal approximation properties, neural networks in different variants and architectures are among the most frequently considered learning methods in systems and control. In contrast to this trend, this project does not ask what machine learning can do for control. Rather we explore the question of how systems and control methods can be beneficial in the design and analysis of training formulations for neural networks.

Specifically, Project P2 considers Neural Ordinary Differential Equations (NODEs) and their explicit discretizations which take the form of Residual Networks (ResNets). We explore how generalization properties of neural networks can be directly considered in the training problems and how system-theoretic dissipativity notions of optimal control problems allow for performance-preserving pruning of trained networks. To this end, we investigate novel data informativity notions tailored to neural networks. Finally, we explore how stochastic control concepts, i.e. feedback policies, can be leveraged to design neural networks with quantifiable generalization properties. The investigated methods are evaluated on benchmark problems stemming from the machine learning literature and on systems and control specific benchmarks developed in the research unit ALeSCo.

Project P6: Benchmarks for active learning in systems and control

Co-Principal Investigator: Prof. Dr.-Ing. Timm Faulwasser

Co-Principal Investigator: Prof. Dr.-Ing. Sandra Hirche

Evaluation and benchmarks are crucial for transparently comparing methods across various fields, including machine learning, optimization, and control systems. Datasets and test problems exist for supervised learning, different branches of control, and robotics. However, a notable gap exists in benchmarks focused on active learning for control of dynamic systems. This project aims to address and bridge this gap by developing a Python package containing representative and challenging scenarios to evaluate and compare active learning techniques for systems and control. We propose evaluation procedures equipped with tailored assessment metrics. To ensure that relevant problem settings are covered, our benchmark focuses on two application domains: multi-energy systems and robotics.

In multi-energy systems, we create scalable test problems for energy distribution systems, integrating real-world datasets, realistic power profiles, and weather data. The benchmark will address varying complexity levels, from known to partially unknown system dynamics of individual nodes to their interaction in constrained network settings. This setting covers stochastic disturbances, parametric drifts, and uncertain or unknown system topologies.

In the robotics domain, we develop benchmarks for autonomous navigation and manipulation tasks for unmanned underwater vehicles and soft robotic arm models. These benchmarks will consider uncertain adjustable levels of availability of information about model parameters, system states and disturbances. Experimentally derived sensor noise and external disturbance models will help to reduce the gap between simulation and reality.

Turnpikes and Dissipativity in Optimal Control

Turnpikes and Dissipativity in Optimal Control

The turnpike phenomenon refers to a similarity property in optimal control problems, i.e., for varying initial conditions of the dynamics and varyign horizon lengths the optimal solutions are structurally similar. Put differently, they stay close to the optimal steady state (a.k.a. the turnpike) in the middle part of the horizon and this part grows as the horizon increases.

Early observations of the phenomenon can be traced back to papers by John von Neumann and Frank P. Ramsey which appeared in the 1930s. The term turnpike was coined in the 1958 book on Linear Programming and Economic Analysis by Dorfman, Solow, and Samuelson. Therein, they coined the term turnpike in optimal control by writing:

"[...] It is exactly like a turnpike paralleled by a network of minor roads. There is a fastest route between any two points; and if the origin and destination are close together and far from the turnpike, the best route may not touch the turnpike. But if the origin and destination are far enough apart, it will always pay to get on to the turnpike and cover distance at the best rate of travel, even if this means adding a little mileage at either end. [...]"

Our research has contributed 

  • to analyzing the turnpike using dissipativity concepts that can be traced back to Jan C. Willems and his seminalt 1971 and 1972 papers,
  • to resolving the long standing issue surrounding the adjoint terminal conditions in infinite-horizon problems. (a.k.a. Halkin´s problem) by showing that under mild assumptions the turnpike phenomenon implies infinite-horizon stability,
  • to the analysis of turnpike in mixed-integer optimal control problems,
  • to extending the turnpipke concepts to generalized infinite horizon attractors (mainfolds and linear subspaces) in optimal control problems for thermodynamic systems and Euler-Lagrange systems, and 
  • to exploiting the turnpike property for the closed-loop analysis of receding-horizon optimal control (a.k.a. model predictive control) with economic objective functions.

In recent research,

  • we have extended turnpike and dissipaticity concepts to stochastic optimal control problems,
  • we used turnpike concepts for closed-loop analysis of model predictive path-following control problems, and
  • we used turnpike concepts to analyze the training of deep neural networks (a.k.a. deep learing) from an optimal control perspective. We also derive explicit depth bounds using turnpike concepts.

 

References

[1] Dorfman, R., Samuelson, P. A., and Solow, R. M., 2012. Linear programming and economic analysis. Courier Corporation.

[2] Willems, J. C., 1971. Least squares stationary optimal control and the algebraic Riccati equation. IEEE Transactions on Automatic Control.

[3] Willems, J. C., 1972. Dissipative dynamical systems part I: General theory. Archive for Rational Mechanics and Analysis.

[4] Willems, J. C., 1972. Dissipative dynamical systems part II: Linear systems with quadratic supply rates. Archive for Rational Mechanics and Analysis.

[5] Faulwasser, T., Korda, M., Jones, C. N., and Bonvin, D., 2014. Turnpike and dissipativity properties in dynamic real-time optimization and economic MPC. In 53rd IEEE Conference on Decision and Control.

[6] Faulwasser, T., Korda, M., Jones, C. N., and Bonvin, D., 2017. On turnpike and dissipativity properties of continuous-time optimal control problems. Automatica.

[7] Faulwasser, T., Grüne, L., and Müller, M. A., 2018. Economic nonlinear model predictive control. Foundations and Trends® in Systems and Control.

[8] Faulwasser, T. and Murray, A., 2020. Turnpike properties in discrete-time mixed-integer optimal control. IEEE Control Systems Letters.

[9] Faulwasser, T. and Bonvin, D., 2017. Exact turnpike properties and economic NMPC. European Journal of Control.

[10] Faulwasser, T., Flaßkamp, K., Ober-Blöbaum, S., Schaller, M., and Worthmann, K., 2022. Manifold turnpikes, trims, and symmetries. Mathematics of Control, Signals, and Systems.

[11] Faulwasser, T. and Grüne, L., 2022. Turnpike properties in optimal control: An overview of discrete-time and continuous-time results. Handbook of Numerical Analysis.

[12] Krügel, L., Faulwasser, T., and Grüne, L., 2023. Local turnpike properties in finite horizon optimal control. In 2023 62nd IEEE Conference on Decision and Control.

[13] Ou, R., Schießl, J., Baumann, M. H., Grüne, L., and Faulwasser, T., 2025. A Polynomial Chaos Approach to Stochastic LQ Optimal Control: Error Bounds and Infinite-Horizon Results. Automatica.

[14] Schießl, J., Baumann, M. H., Faulwasser, T., and Grüne, L., 2024. On the relationship between stochastic turnpike and dissipativity notions. IEEE Transactions on Automatic Control.

[15] Faulwasser, T., Hempel, A. J., and Streif, S., 2024. On the turnpike to design of deep neural networks: Explicit depth bounds. IFAC Journal of Systems and Control.

[16] Püttschneider, J. and Faulwasser, T., 2024. On dissipativity of cross-entropy loss in training ResNets. arXiv Preprint.

Data-Driven Control for Deterministic and Stochastic Systems

Data-Driven Control for Deterministic and Stochastic Systems

Dynamic systems can often be described using algebraic and/or differential equations derived from first principles. We are interested in describing behaviors of various systems using available data in form of input-output measurements and/or disturbance estimates. Specifically, we focus on developing novel model-free control approaches and benchmarks to test their performance against either existing methods or model-based controllers.

In many real-world applications, stochastic disturbances pose significant challenges, such as distributed energy systems facing uncertain wind speed and renewable energy generation, or building control systems dealing with uncertain weather conditions and occupancy. The presence of stochastic disturbances can severely deteriorate both the performance and safety of the system. However, extending the framework of data-driven control to stochastic systems—where uncertainties must be explicitly accounted for—remains an open problem. In this context, another focus of our work centers on addressing this challenge.

References

[1] Ou, R., Pan, G., and Faulwasser, T., 2025. A stochastic fundamental lemma with reduced disturbance data requirements, arXiv Preprint.

[2] Molodchyk, O., Schmitz, P., Engelmann, A., Worthmann, K., and Faulwasser, T., 2025. Towards Data-Driven Multi-Stage OPF. arXiv Preprint, accepted for IEEE PES PowerTech Conference.

[3] Pan, G., Ou, R., and Faulwasser, T., 2024. On data-driven stochastic output-feedback predictive control, IEEE Transactions on Automatic Control.

[4] Molodchyk, O., and Faulwasser, T., 2024. Exploring the links between the fundamental lemma and kernel regression, IEEE Control Systems Letters.

[5] Özmeteler, M. B., Bilgic, D., Pan, G., Koch, A., and Faulwasser, T., 2024. Data-driven uncertainty propagation for stochastic predictive control of multi-energy systems, European Journal of Control.

[6] Faulwasser, T., Ou, R., Pan, G., Schmitz, P., and Worthmann, K., 2023. Behavioral theory for stochastic systems? A data-driven journey from Willems to Wiener and back again, Annual Reviews in Control.

[7] Ou, R., Pan, G., and Faulwasser, T., 2023. Data-driven multiple shooting for stochastic optimal control, IEEE Control Systems Letters.

[8] Pan, G., and Faulwasser, T., 2023. Distributionally robust uncertainty quantification via data-driven stochastic optimal control, IEEE Control Systems Letters.

[9] Pan, G., Ou, R., and Faulwasser, T., 2023. On a stochastic fundamental lemma and its use for data-driven optimal control, IEEE Transactions on Automatic Control.

[10] Bilgic, D., Koch, A., Pan, G., and Faulwasser, T., 2022. Toward data-driven predictive control of multi-energy distribution systems, Electric Power Systems Research.

Control and Optimization of Port-Hamiltonian Systemsc Systems

Control and Optimization of Port-Hamiltonian Systems

Physics-based modelling leads to port-Hamiltonian structures [1-2]. These models consist of constitutive components: energy storage, energy dissipation, and ports which allows to transfer energy over system boundaries. Our research, supported by Deutsche Forschungsgemeinschaft (DFG), aims to exploit the structure of port-Hamiltonian systems in the realm of optimal and data-driven control.

Distributed Optimization and Distributed MPC

Distributed Optimization and Distributed MPC

Numerical optimization is key in the operation of complex systems. For different reasons such as resilience, data privacy and performance one may be interested in distributing numerical optimization over different nodes. In the realm of Model Predictive Control (MPC) this distributed optimization arises in the context of distributed MPC (DMPC).

We conduct research on distributed non-convex optimization and on distributed MPC for linear and nonlinear systems. 

 

Embedded cooperative distributed model predictive control applied to a team of hovercraft

Embedded cooperative distributed model predictive control applied to a team of hovercraft

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References

[1] Stomberg, G., Engelmann, A. and Faulwasser, T., 2022. A compendium of optimization algorithms for distributed linear-quadratic MPC. at-Automatisierungstechnik.

[2] Stomberg, G., Ebel, H., Faulwasser, T. and Eberhard, P., 2023. Cooperative distributed MPC via decentralized real-time optimization: Implementation results for robot formations. Control Engineering Practice.

[3] Stomberg, G., Engelmann, A., Diehl, M. and Faulwasser, T., 2024. Decentralized real-time iterations for distributed nonlinear model predictive control. arXiv Preprint.

[4] Stomberg, G., Schwan, R., Grillo, A., Jones C. N. and Faulwasser, T., 2024. Cooperative distributed model predictive control for embedded systems: Experiments with hovercraft formations. arXiv Preprint.

[5] Stomberg, G., Raetsch, M., Engelmann A. and Faulwasser T. ,2024. Large problems are not necessarily hard: A case study on distributed NMPC paying off. arXiv Preprint.

[6] Engelmann, A., Jiang, Y., Houska, B., and Faulwasser, T. ,2020. Decomposition of nonconvex optimization via bi-level distributed ALADIN. IEEE Transactions on Control of Network Systems.

[7] Engelmann, A., Stomberg, G., and Faulwasser, T. ,2021. An essentially decentralized interior point method for control. In 2021 60th IEEE Conference on Decision and Control (CDC).

[8] Stomberg G., Engelmann A., and Faulwasser T. ,2022. Decentralized non-convex optimization via bi-level SQP and ADMM. In 2022 IEEE 61st Conference on Decision and Control (CDC).

[9] Engelmann A., Jiang Y., Benner H., Ou R., Houska B., and Faulwasser T. ,2022. ALADIN‐α—An open‐source MATLAB toolbox for distributed non‐convex optimization. Optimal Control Applications and Methods.

Optimal Power Flow (OPF)

Optimal Power Flow Problems

Optimal Power Flow (OPF) problems are of crucial importance for the operation of electrical energy grids. A prime indicator are the steadily increasing costs for generator redsipatch and curative grid actions in Germany –cf. the monitoring report by the German grid authority (Bundesnetzagentur BNA)– as these operational decisions are based on the solution of OPF problems. In this context, we investigate novel numerical methods including stochastic OPF formulations and distributed solution algorithms. The former is driven by the increasing share of volatile renwables in the energy mix, which have to be modelled by non-Gaussian distributions. We use Polynomial Chaos Expansions to achieve a tractable reformulation. The modelling of such uncertainties is one of our research topics in the Collaborative Research Center/Transregio CRC/TRR 391 Spatio-temporal Statistics for the Transition of Energy and Transport.

We also investigate distributed optimization algorithms to solve optimal power flow problems in stationary and time coupled multi-stage formulations as well as the application of design of experiments to enable in-operation estimation of parameters. 

References

[1] Mühlpfordt, T., Roald, L., Hagenmeyer, V., Faulwasser, T., & Misra, S. (2019). Chance-constrained AC optimal power flow: A polynomial chaos approach. IEEE Transactions on Power Systems, 34(6), 4806-4816.

[2] Faulwasser, T., Engelmann, A., Mühlpfordt, T., & Hagenmeyer, V. (2018). Optimal power flow: an introduction to predictive, distributed and stochastic control challenges. at-Automatisierungstechnik, 66(7), 573-589.

[3] Mühlpfordt, T., Zahn, F., Hagenmeyer, V., & Faulwasser, T. (2020). PolyChaos. jl—A Julia package for polynomial chaos in systems and control. IFAC-PapersOnLine, 53(2), 7210-7216.

[4] Mühlpfordt, T., Faulwasser, T., & Hagenmeyer, V. (2018). A generalized framework for chance-constrained optimal power flow. Sustainable Energy, Grids and Networks, 16, 231-242.

[5] Engelmann, A., Jiang, Y., Mühlpfordt, T., Houska, B., & Faulwasser, T. (2018). Toward distributed OPF using ALADIN. IEEE Transactions on Power Systems, 34(1), 584-594.

[6] Engelmann, A., Jiang, Y., Houska, B., & Faulwasser, T. (2020). Decomposition of nonconvex optimization via bi-level distributed ALADIN. IEEE Transactions on Control of Network Systems, 7(4), 1848-1858.

[7] Engelmann, A., Jiang, Y., Benner, H., Ou, R., Houska, B., & Faulwasser, T. (2022). ALADIN‐a—An open‐source MATLAB toolbox for distributed non‐convex optimization. Optimal Control Applications and Methods, 43(1), 4-22.

[8] Murray, A., Engelmann, A., Hagenmeyer, V., & Faulwasser, T. (2018). Hierarchical distributed mixed-integer optimization for reactive power dispatch. IFAC-PapersOnLine, 51(28), 368-373.

[9] Du, X., Engelmann, A., Jiang, Y., Faulwasser, T., & Houska, B. (2020). Optimal experiment design for ac power systems admittance estimation. IFAC-PapersOnLine, 53(2), 13311-13316.

[10] Stomberg, G., Raetsch, M., Engelmann, A., & Faulwasser, T. (2024). Large problems are not necessarily hard: A case study on distributed NMPC paying off. arXiv preprint arXiv:2411.05627.

 

 

 

Co-Design of Control and Communication

Co-Design of Control and Communication

The rapid advancements in communication technologies, particularly with the rollout of 5G and future 6G networks, offer a transformative opportunity to integrate high-speed, low-latency, and reliable communication into modern control systems. A co-design approach of communication and control systems promises transformative benefits that significantly enhance performance, reliability, and scalability across various applications. This integration lays the foundation for cutting-edge applications, including autonomous systems, industrial automation, smart cities and more.

Traditionally, control and communication systems have been designed separately, oftenresulting in inefficiencies and suboptimal control performance. In such decoupled systems, communication resources and control processes may compete for bandwidth or processing power, leading to delays, increased latency, and even instabilities. As systems become more complex and interdependent, particularly with the advent of autonomous vehicles, smart grids, and robotics, the separation between control and communication becomes less feasible.

In essence, co-design helps eliminate the inefficiencies inherent in traditional decoupled approaches and ensures that both control and communication work together seamlessly, enabling faster decision-making, increased reliability, and better scalability.

One recent contribution of our group in the co-design of control and communication is the development of an event-triggered nonlinear model predictive controller (ET-MPC) over a 6G research platform [1]. This approach integrates advanced control algorithms with the high-performance communication capabilities of6G networks, enabling dynamic and efficient control decisions in real-time applications. By using event-triggered mechanisms, the system can reduce unnecessary communication while maintaining control performance, thus making more efficient use of available resources in a 6G network context.