@article{59740, abstract = {{ABSTRACTIn this contribution, we propose an innovative method for determining optimal control sequences for nonlinear systems with partially unknown dynamics, which further expands our previous work. Within the paradigm of model‐based design, the practicality and safety of commissioning feedforward controls and feedback controllers have priority. Our approach leverages probabilistic Gaussian processes to adjust for model inaccuracies from measured system data. This differs from conventional approaches that involve complicated analytical modeling and may entail a substantial time investment to acquire expertise and may prove impractical. Consequently, we address the limitations inherent in traditional design methodologies. Our research focuses on the formulation and solution of the hybrid1 optimal control problem using probabilistic state predictions and multiple shooting. This ensures adaptability, data efficiency, and resilience against uncertainties in system dynamics. These attributes are empirically substantiated through experimental validation on a chaotic and highly sensitive dynamical system—a double pendulum on a cart. Our methodology unfolds as an iterative learning process, systematically exploring diverse controls, accumulating data within each iteration, and refining the control strategy until the desired task is accomplished. The adoption of the two‐degree‐of‐freedom control structure allows for the distinct consideration of the feedforward and the feedback control signal. For the latter, we employ a time‐variant, linear quadratic regulator (LQR) designed to stabilize the system around its target trajectory. Furthermore, we integrate a probabilistic long‐term prediction through the unscented transform, enabling systematic anticipation of safety‐critical violations. Detailed insights into relevant implementation aspects are provided. To ascertain the real‐world applicability, we present an exemplary application involving a double pendulum on a cart. The objective is to bring the pendulum arms from the lower stable to the upper unstable equilibrium by horizontally moving the cart and subsequently stabilize them. In this scenario, we assume that the centrifugal forces, crucial to the system dynamics, have not been accurately modeled and must be learned from data. Solving the control task took only 5 iterations and 1 h of computation time, which surpasses our previous work [2], where we used the purely data‐driven PILCO framework and required 27 iterations and 57 h of computation time. The time of interaction with the system decreased by and the computation time is lowered by . It demonstrates significant practical applicability for commissioning control systems.}}, author = {{Hesse, Michael and Schwarzer, Luis and Timmermann, Julia and Trächtler, Ansgar}}, issn = {{1617-7061}}, journal = {{PAMM}}, number = {{2}}, publisher = {{Wiley}}, title = {{{Robust and Efficient Hybrid Optimal Control via Gaussian Process Regression and Multiple Shooting With Experimental Validation on a Double Pendulum on a Cart}}}, doi = {{10.1002/pamm.70004}}, volume = {{25}}, year = {{2025}}, } @book{61118, abstract = {{Im Zuge der Digitalisierung erfahren maschinelles Lernen und datengetriebene Methoden derzeit eine große Aufmerksamkeit in Wissenschaft und Industrie. Es fehlt jedoch an Grundlagenwissen und Verständnis, wie die datengetriebenen Methoden der Informatik mit bewährten modellbasierten Ingenieursmethoden wie dem modellbasierten Entwurf in der Mechatronik und Methoden der Regelungstechnik sinnvoll kombiniert werden können, um hybride Modelle zu erhalten. Diese ingenieurwissenschaftlichen Methoden basieren auf physikalischen Verhaltensmodellen, die eine besonders verdichtete und interpretierbare Darstellung von Wissen darstellen und insbesondere kausale Zusammenhänge beschreiben. Für spezifische regelungstechnische Anwendungen gibt es umfangreiches Vorwissen in Form von bekannten Strukturen und Informationen, wie z.B. (Teil-)Modelle oder Parametersätze, die auch bei der Anwendung von Methoden wie dem maschinellen Lernen genutzt werden sollten. Eine solche sinnvolle systematische Verknüpfung ist wissenschaftlich, insbesondere im Hinblick auf die industrielle Anwendung, noch nicht ausreichend untersucht worden und sehr vielversprechend. In diesem Beitrag werden die Ergebnisse der Nachwuchsforschungsgruppe DART – Datengetriebene Methoden in der Regelungstechnik vorgestellt. Das Hauptziel war es, die synergetische Kombination von modell- und datengetriebenen Methoden für regelungstechnische Aufgaben zu erforschen und es werden alle wichtigen Forschungsergebnisse aber auch die verwendeten Grundprinzipien des maschinellen Lernens in diesem Beitrag dargestellt.}}, author = {{Timmermann, Julia and Götte, Ricarda-Samantha and Junker, Annika and Hesse, Michael and Schwarzer, Luis}}, publisher = {{HNI Verlagsschriftenreihe}}, title = {{{DART - Datengetriebene Methoden in der Regelungstechnik}}}, doi = {{10.17619/UNIPB/1-2305}}, volume = {{Band 430}}, year = {{2025}}, } @article{57893, abstract = {{AbstractControl engineering applications usually require a model that accurately represents the dynamics of the system. In addition to classical physical modeling, powerful data‐driven approaches are gaining popularity. However, the resulting models may not be ideal for control design due to their black‐box structure, which inherently limits interpretability. Formulating the system dynamics in port‐Hamiltonian form is highly beneficial, as its valuable property of passivity enables the straightforward design of globally stable controllers while ensuring physical interpretability. In a recently published article, we presented a method for data‐driven inference of port‐Hamiltonian models for complex mechatronic systems, requiring only fundamental physical prior knowledge. The resulting models accurately represent the nonlinear dynamics of the considered systems and are physically interpretable. In this contribution, we advance our previous work by including two key elements. Firstly, we demonstrate the application of the above described data‐driven PCHD models for controller design. Preserving the port‐Hamiltonian form in the closed loop not only guarantees global stability and robustness but also ensures desired speed and damping characteristics. Since control systems based on output measurements, which are continuously measured during operation due to the feedback structure, we secondly aim to use this data. Thus, we augment the existing modeling strategy with an intelligent adaptation approach to address uncertainties and (un)predictable system changes in mechatronic systems throughout their lifecycle, such as the installation of new components, wear, or temperature fluctuations during operation. Our proposed algorithm for recursively calculated data‐driven port‐Hamiltonian models utilizes a least‐squares approach with extensions such as automatically adjusting the forgetting factor and controlling the covariance matrix trace. We demonstrate the results through model‐based application on an academic example and experimental validation on a test bench.}}, author = {{Junker, Annika and Timmermann, Julia and Trächtler, Ansgar}}, issn = {{1617-7061}}, journal = {{PAMM}}, number = {{1}}, publisher = {{Wiley}}, title = {{{Adaptive Data‐Driven Models in Port‐Hamiltonian Form for Control Design}}}, doi = {{10.1002/pamm.202400154}}, volume = {{25}}, year = {{2024}}, } @article{59051, abstract = {{Model‐based state observers require high‐quality models to deliver accurate state estimates. However, due to time or cost shortage, modeling simplifications or numerical issues, models often have severe inaccuracies that may lead to insufficient and deficient control. Instead of attempting to iteratively model these deviations, we address the challenge by the concept of joint estimation. Thus, we assume a linear combination of suitable functions to approximate the inaccuracies. The parameters of the linear combination are supposed to be time invariant and augment the model's state. Subsequently, the parameters can be identified simultaneously to the states within the observer. Referring to the principle of Occam's razor, the parameters are claimed to be sparse. Our former work shows that estimating states and model inaccuracies simultaneously by a sparsity promoting unscented Kalman filter yields not only high accuracy but also provides interpretable representations of underlying inaccuracies. Based on this work, our contribution is twofold: First, we apply our approach finally on a real‐world test bench, namely a golf robot. Within the experimental setting, we investigate closed loop behavior as well as how suitable functions need to be chosen to approximate the inaccuracies in a physically interpretable way. Results do not only provide high state estimation accuracy but also meaningful insights into the system's inaccuracies. Second, we discuss and establish a method to automatically adapt and update the model based on collected data of the linear combination during operation. Examining past parameter estimates by principal component analysis, a moving window is utilized to extract the most dominant functions. These are kept characterizing the model inaccuracies, while nondominant functions are automatically neglected and refilled with novel function candidates. After analysis and rebuilding, this updated function set is subsequently fed back into the joint estimation loop and deployed for further estimation. Hence, we give a holistic paradigm of how to analyze and combat model inaccuracies while ensuring high state estimation accuracy. Within this setting, we once more investigate closed loop behavior and yield promising results. In conclusion, we show that the proposed observer provides a helpful tool to guarantee high estimation accuracy for models with severe inaccuracies or for situations with occurring deviations during operation, for example, due to mechanical wear or temperature changes.}}, author = {{Götte, Ricarda-Samantha and Timmermann, Julia}}, issn = {{1617-7061}}, journal = {{PAMM}}, number = {{1}}, publisher = {{Wiley}}, title = {{{Online Learning With Joint State and Model Estimation}}}, doi = {{10.1002/pamm.202400080}}, volume = {{25}}, year = {{2024}}, } @inproceedings{34171, abstract = {{State estimation when only a partial model of a considered system is available remains a major challenge in many engineering fields. This work proposes a joint, square-root unscented Kalman filter to estimate states and model uncertainties simultaneously by linear combinations of physics-motivated library functions. Using a sparsity promoting approach, a selection of those linear combinations is chosen and thus an interpretable model can be extracted. Results indicate a small estimation error compared to a traditional square-root unscented Kalman filter and exhibit the enhancement of physically meaningful models.}}, author = {{Götte, Ricarda-Samantha and Timmermann, Julia}}, booktitle = {{12th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2022)}}, keywords = {{joint estimation, unscented transform, Kalman filter, sparsity, data-driven, compressed sensing}}, location = {{Canberra, Australien}}, number = {{1}}, pages = {{85--90}}, title = {{{Estimating States and Model Uncertainties Jointly by a Sparsity Promoting UKF}}}, doi = {{https://doi.org/10.1016/j.ifacol.2023.02.015}}, volume = {{56}}, year = {{2023}}, } @inproceedings{44326, abstract = {{Low-quality models that miss relevant dynamics lead to major challenges in modelbased state estimation. We address this issue by simultaneously estimating the system’s states and its model inaccuracies by a square root unscented Kalman filter (SRUKF). Concretely, we augment the state with the parameter vector of a linear combination containing suitable functions that approximate the lacking dynamics. Presuming that only a few dynamical terms are relevant, the parameter vector is claimed to be sparse. In Bayesian setting, properties like sparsity are expressed by a prior distribution. One common choice for sparsity is a Laplace distribution. However, due to disadvantages of a Laplacian prior in regards to the SRUKF, the regularized horseshoe distribution, a Gaussian that approximately features sparsity, is applied instead. Results exhibit small estimation errors with model improvements detected by an automated model reduction technique.}}, author = {{Götte, Ricarda-Samantha and Timmermann, Julia}}, booktitle = {{IFAC-PapersOnLine}}, keywords = {{joint estimation, unscented Kalman filter, sparsity, Laplacian prior, regularized horseshoe, principal component analysis}}, location = {{Yokohama, Japan}}, number = {{2}}, pages = {{869--874}}, title = {{{Approximating a Laplacian Prior for Joint State and Model Estimation within an UKF}}}, volume = {{56}}, year = {{2023}}, } @inproceedings{48482, author = {{Götte, Ricarda-Samantha and Klusmann, Jo Noel and Timmermann, Julia}}, booktitle = {{Proceedings - 33. Workshop Computational Intelligence: Berlin, 23.-24. November 2023}}, location = {{Berlin, Germany}}, pages = {{113--123}}, title = {{{Data-driven identification of disturbances using a sliding mode observer}}}, doi = {{10.5445/KSP/1000162754}}, year = {{2023}}, } @inproceedings{48476, author = {{Hesse, Michael and Timmermann, Julia and Trächtler, Ansgar}}, booktitle = {{2023 European Control Conference (ECC)}}, publisher = {{IEEE}}, title = {{{Hybrid Optimal Control for Dynamical Systems using Gaussian Process Regression and Unscented Transform*}}}, doi = {{10.23919/ecc57647.2023.10178368}}, year = {{2023}}, } @article{50070, author = {{Junker, Annika and Pape, Keno Egon Friedrich and Timmermann, Julia and Trächtler, Ansgar}}, issn = {{2405-8963}}, journal = {{IFAC-PapersOnLine}}, keywords = {{General Medicine}}, number = {{3}}, pages = {{625--630}}, publisher = {{Elsevier BV}}, title = {{{Adaptive Koopman-Based Models for Holistic Controller and Observer Design}}}, doi = {{10.1016/j.ifacol.2023.12.094}}, volume = {{56}}, year = {{2023}}, } @inproceedings{42238, author = {{Junker, Annika and Fittkau, Niklas and Timmermann, Julia and Trächtler, Ansgar}}, booktitle = {{2022 Sixth IEEE International Conference on Robotic Computing (IRC)}}, location = {{Naples, Italy}}, publisher = {{IEEE}}, title = {{{Autonomous Golf Putting with Data-Driven and Physics-Based Methods}}}, doi = {{10.1109/irc55401.2022.00031}}, year = {{2023}}, } @inproceedings{26539, abstract = {{In control design most control strategies are model-based and require accurate models to be applied successfully. Due to simplifications and the model-reality-gap physics-derived models frequently exhibit deviations from real-world-systems. Likewise, purely data-driven methods often do not generalise well enough and may violate physical laws. Recently Physics-Guided Neural Networks (PGNN) and physics-inspired loss functions separately have shown promising results to conquer these drawbacks. In this contribution we extend existing methods towards the identification of non-autonomous systems and propose a combined approach PGNN-L, which uses a PGNN and a physics-inspired loss term (-L) to successfully identify the system's dynamics, while maintaining the consistency with physical laws. The proposed method is demonstrated on two real-world nonlinear systems and outperforms existing techniques regarding complexity and reliability.}}, author = {{Götte, Ricarda-Samantha and Timmermann, Julia}}, booktitle = {{2022 3rd International Conference on Artificial Intelligence, Robotics and Control (AIRC)}}, keywords = {{data-driven, physics-based, physics-informed, neural networks, system identification, hybrid modelling}}, location = {{Cairo, Egypt}}, pages = {{67--76}}, title = {{{Composed Physics- and Data-driven System Identification for Non-autonomous Systems in Control Engineering}}}, doi = {{10.1109/AIRC56195.2022.9836982}}, year = {{2022}}, } @inproceedings{31066, abstract = {{While trade-offs between modeling effort and model accuracy remain a major concern with system identification, resorting to data-driven methods often leads to a complete disregard for physical plausibility. To address this issue, we propose a physics-guided hybrid approach for modeling non-autonomous systems under control. Starting from a traditional physics-based model, this is extended by a recurrent neural network and trained using a sophisticated multi-objective strategy yielding physically plausible models. While purely data-driven methods fail to produce satisfying results, experiments conducted on real data reveal substantial accuracy improvements by our approach compared to a physics-based model. }}, author = {{Schön, Oliver and Götte, Ricarda-Samantha and Timmermann, Julia}}, booktitle = {{14th IFAC Workshop on Adaptive and Learning Control Systems (ALCOS 2022)}}, keywords = {{neural networks, physics-guided, data-driven, multi-objective optimization, system identification, machine learning, dynamical systems}}, location = {{Casablanca, Morocco}}, number = {{12}}, pages = {{19--24}}, title = {{{Multi-Objective Physics-Guided Recurrent Neural Networks for Identifying Non-Autonomous Dynamical Systems}}}, doi = {{https://doi.org/10.1016/j.ifacol.2022.07.282}}, volume = {{55}}, year = {{2022}}, } @inproceedings{29803, abstract = {{Ultrasonic wire bonding is a solid-state joining process used to form electrical interconnections in micro and power electronics and batteries. A high frequency oscillation causes a metallurgical bond deformation in the contact area. Due to the numerous physical influencing factors, it is very difficult to accurately capture this process in a model. Therefore, our goal is to determine a suitable feed-forward control strategy for the bonding process even without detailed model knowledge. We propose the use of batch constrained Bayesian optimization for the control design. Hence, Bayesian optimization is precisely adapted to the application of bonding: the constraint is used to check one quality feature of the process and the use of batches leads to more efficient experiments. Our approach is suitable to determine a feed-forward control for the bonding process that provides very high quality bonds without using a physical model. We also show that the quality of the Bayesian optimization based control outperforms random search as well as manual search by a user. Using a simple prior knowledge model derived from data further improves the quality of the connection. The Bayesian optimization approach offers the possibility to perform a sensitivity analysis of the control parameters, which allows to evaluate the influence of each control parameter on the bond quality. In summary, Bayesian optimization applied to the bonding process provides an excellent opportunity to develop a feedforward control without full modeling of the underlying physical processes.}}, author = {{Hesse, Michael and Hunstig, Matthias and Timmermann, Julia and Trächtler, Ansgar}}, booktitle = {{Proceedings of the 11th International Conference on Pattern Recognition Applications and Methods (ICPRAM)}}, isbn = {{978-989-758-549-4}}, keywords = {{Bayesian optimization, Wire bonding, Feed-forward control, model-free design}}, location = {{Online}}, pages = {{383--394}}, title = {{{Batch Constrained Bayesian Optimization for UltrasonicWire Bonding Feed-forward Control Design}}}, year = {{2022}}, } @inproceedings{26389, abstract = {{Within this work, we investigate how data-driven numerical approximation methods of the Koopman operator can be used in practical control engineering applications. We refer to the method Extended Dynamic Mode Decomposition (EDMD), which approximates a nonlinear dynamical system as a linear model. This makes the method ideal for control engineering applications, because a linear system description is often assumed for this purpose. Using academic examples, we simulatively analyze the prediction performance of the learned EDMD models and show how relevant system properties like stability, controllability, and observability are reflected by the EDMD model, which is a critical requirement for a successful control design process. Subsequently, we present our experimental results on a mechatronic test bench and evaluate the applicability to the control engineering design process. As a result, the investigated methods are suitable as a low-effort alternative for the design steps of model building and adaptation in the classical model-based controller design method.}}, author = {{Junker, Annika and Timmermann, Julia and Trächtler, Ansgar}}, booktitle = {{2022 3rd International Conference on Artificial Intelligence, Robotics and Control (AIRC 2022)}}, isbn = {{978-1-6654-5946-4}}, keywords = {{Koopman Operator, Nonlinear Control, Extended Dynamic Mode Decomposition, Hybrid Modelling}}, location = {{Cairo, Egypt}}, pages = {{1--9}}, title = {{{Data-Driven Models for Control Engineering Applications Using the Koopman Operator}}}, doi = {{10.1109/AIRC56195.2022.9836980}}, year = {{2022}}, } @inproceedings{34011, author = {{Junker, Annika and Fittkau, Niklas and Timmermann, Julia and Trächtler, Ansgar}}, booktitle = {{Proceedings - 32. Workshop Computational Intelligence: Berlin, 1. - 2. Dezember 2022}}, location = {{Berlin, Germany}}, pages = {{119--124}}, title = {{{Autonomes Putten mittels datengetriebener und physikbasierter Methoden}}}, doi = {{10.5445/KSP/1000151141}}, year = {{2022}}, } @article{50071, author = {{Junker, Annika and Timmermann, Julia and Trächtler, Ansgar}}, issn = {{2405-8963}}, journal = {{IFAC-PapersOnLine}}, keywords = {{Control and Systems Engineering}}, number = {{12}}, pages = {{389--394}}, publisher = {{Elsevier BV}}, title = {{{Learning Data-Driven PCHD Models for Control Engineering Applications*}}}, doi = {{10.1016/j.ifacol.2022.07.343}}, volume = {{55}}, year = {{2022}}, } @inbook{22984, author = {{Lüke, Christopher and Timmermann, Julia and Kessler, Jan Henning and Trächtler, Ansgar}}, booktitle = {{Steigerung der Intelligenz mechatronischer Systeme}}, pages = {{153--192}}, publisher = {{Springer Vieweg}}, title = {{{Intelligente Steuerungen und Regelungen}}}, volume = {{1}}, year = {{2018}}, } @article{22996, abstract = {{The effective control design of a dynamical system traditionally relies on a high level of system understanding, usually expressed in terms of an exact physical model. In contrast to this, reinforcement learning adopts a data-driven approach and constructs an optimal control strategy by interacting with the underlying system. To keep the wear of real-world systems as low as possible, the learning process should be short. In our research, we used the state-of-the-art reinforcement learning method PILCO to design a feedback control strategy for the swing-up of the double pendulum on a cart with remarkably few test iterations at the test bench. PILCO stands for “probabilistic inference for learning control” and requires only few expert knowledge for learning. To achieve the swing-up of a double pendulum on a cart to its upper unstable equilibrium position, we introduce additional state restrictions to PILCO, so that the limited cart distance can be taken into account. Thanks to these measures, we were able to learn the swing up at the real test bench for the first time and in only 27 learning iterations.}}, author = {{Hesse, Michael and Timmermann, Julia and Hüllermeier, Eyke and Trächtler, Ansgar}}, journal = {{Procedia Manufacturing}}, pages = {{15 -- 20}}, title = {{{A Reinforcement Learning Strategy for the Swing-Up of the Double Pendulum on a Cart}}}, volume = {{24}}, year = {{2018}}, } @inproceedings{23005, author = {{Xu, Ke and Timmermann, Julia and Trächtler, Ansgar}}, booktitle = {{Proc. Advanced Intelligent Mechatronics (AIM)}}, publisher = {{IEEE}}, title = {{{Nonlinear Model Predictive Control with Discrete Mechanics and Optimal Control}}}, year = {{2017}}, } @inproceedings{23006, author = {{Xu, Ke and Timmermann, Julia and Trächtler, Ansgar}}, booktitle = {{Proc. 20th IFAC World Congress}}, title = {{{Swing-up of the moving double pendulum on a cart with simulation based LQR-Trees}}}, year = {{2017}}, }