@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}}, } @phdthesis{58164, abstract = {{Der modellbasierte Regelungsentwurf erfordert eine möglichst genaue Kenntnis über das dynamische Verhalten des zugrunde liegenden physikalischen Systems. Durch maschinelle Lernverfahren besteht das Potenzial den Modellierungsaufwand im Vergleich zum klassischen Vorgehen zu reduzieren, indem physikalisches Vorwissen und an Messdaten trainierte Modelle effektiv zusammengeführt werden. Diese Dissertation entwickelt Methoden zur datengetriebenen Bestimmung von Modellen für den Regelungsentwurf nichtlinearer mechatronischer Systeme. Dazu wird die regelungstechnische Anwendbarkeit von Koopman-Operator-basierten Verfahren analysiert, die nichtlineare Dynamiken durch lineare Modelle approximieren. Darüber hinaus wird ein neuartiges Verfahren zur datengetriebenen Bestimmung von Port-Hamilton-Modellen entwickelt, die Energiezusammenhänge plausibel abbilden und sich unmittelbar für einen passivitätsbasierten Regelungsentwurf verwenden lassen. Zudem werden Ansätze zur automatischen Aktualisierung des im Regelkreis verwendeten Streckenmodells bei Modellunsicherheiten oder auftretenden Veränderungen der Systemdynamik vorgestellt. Experimentelle sowie simulative Untersuchungen demonstrieren die herausragende Prädiktionsgenauigkeit der datengetriebenen Modelle und die hohe Regelgüte. Die Ergebnisse dieser Dissertation leisten einen bedeutenden Beitrag, weil die datengetriebenen Modelle eine aus regelungstechnischer Sicht verwertbare Form aufweisen. Sie sind physikalisch interpretierbar und lassen sich nahtlos in bestehende Analyse- und Entwurfsmethoden einbinden. Dies eröffnet neue Perspektiven für zukünftige Anwendungen und Weiterentwicklungen.}}, author = {{Junker, Annika}}, isbn = {{9783947647477}}, publisher = {{Heinz Nixdorf Institut}}, title = {{{Datengetriebene Modellbildung für nichtlineare mechatronische Systeme in regelungstechnisch verwertbarer Form}}}, doi = {{10.17619/UNIPB/1-2158}}, volume = {{Band 428}}, year = {{2024}}, } @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}}, } @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{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}}, }