arXiv subjects

Julia Timmermann

Publications and source records attributed to Julia Timmermann.

8 recordsLinked to original sources

arXiv2022

Approximating a Laplacian Prior for Joint State and Model Estimation within an UKF

A major challenge in state estimation with model-based observers are low-quality models that lack of relevant dynamics. We address this issue by simultaneously estimating the system's states and its model uncertainties by a square root UKF. Concretely, we extend the state by 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 some disadvantages of a Laplacian prior, the regularized horseshoe distribution, a Gaussian that approximately features sparsity, is applied. Results exhibit small estimation errors with model improvements detected by an automated model reduction technique.

eess.SP↗

arXiv2022

Adaptive Koopman-Based Models for Holistic Controller and Observer Design

We present a method to obtain a data-driven Koopman operator-based model that adapts itself during operation and can be straightforwardly used for the controller and observer design. The adaptive model is able to accurately describe different state-space regions and additionally consider unpredictable system changes that occur during operation. Furthermore, we show that this adaptive model is applicable to state-space control, which requires complete knowledge of the state vector. For changing system dynamics, the state observer therefore also needs to have the ability to adapt. To the best of our knowledge, there have been no approaches presently available that holistically use an adaptive Koopman-based plant model for the state-space design of both the controller and observer. We demonstrate our method on a test rig: controller and observer adequately adapt during operation, so that outstanding control performance is achieved even in the case of strong occuring systems changes.

math.OC↗

arXiv2022

Autonomous Golf Putting with Data-Driven and Physics-Based Methods

We are developing a self-learning mechatronic golf robot using combined data-driven and physics-based methods, to have the robot autonomously learn to putt the ball from an arbitrary point on the green. Apart from the mechatronic control design of the robot, this task is accomplished by a camera system with image recognition and a neural network for predicting the stroke velocity vector required for a successful hole-in-one. To minimize the number of time-consuming interactions with the real system, the neural network is pretrained by evaluating basic physical laws on a model, which approximates the golf ball dynamics on the green surface in a data-driven manner. Thus, we demonstrate the synergetic combination of data-driven and physics-based methods on the golf robot as a mechatronic example system.

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arXiv2022

Estimating States and Model Uncertainties Jointly by a Sparsity Promoting UKF

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.

eess.SP↗

arXiv2022

Multi-Objective Physics-Guided Recurrent Neural Networks for Identifying Non-Autonomous Dynamical Systems

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.

eess.SY↗

arXiv2022

Learning Data-Driven PCHD Models for Control Engineering Applications

The design of control engineering applications usually requires a model that accurately represents the dynamics of the real system. In addition to classical physical modeling, powerful data-driven approaches are increasingly used. However, the resulting models are not necessarily in a form that is advantageous for controller design. In the control engineering domain, it is highly beneficial if the system dynamics is given in PCHD form (Port-Controlled Hamiltonian Systems with Dissipation) because globally stable control laws can be easily realized while physical interpretability is guaranteed. In this work, we exploit the advantages of both strategies and present a new framework to obtain nonlinear high accurate system models in a data-driven way that are directly in PCHD form. We demonstrate the success of our method by model-based application on an academic example, as well as experimentally on a test bed.

eess.SY↗

arXiv2021

Data-Driven Models for Control Engineering Applications Using the Koopman Operator

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.

eess.SY↗

arXiv2021

Composed Physics- and Data-driven System Identification for Non-autonomous Systems in Control Engineering

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.

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