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Towards data-driven stochastic predictive control
(2023-08-02) Pan, Guanru; Ou, Ruchuan; Faulwasser, Timm
Data-driven predictive control based on the fundamental lemma by Willems et al. is frequently considered for deterministic LTI systems subject to measurement noise. However, little has been done on data-driven stochastic control. In this paper, we propose a data-driven stochastic predictive control scheme for LTI systems subject to possibly unbounded additive process disturbances. Based on a stochastic extension of the fundamental lemma and leveraging polynomial chaos expansions, we construct a data-driven surrogate optimal control problem (OCP). Moreover, combined with an online selection strategy of the initial condition of the OCP, we provide sufficient conditions for recursive feasibility and for stability of the proposed data-driven predictive control scheme. Finally, two numerical examples illustrate the efficacy and closed-loop properties of the proposed scheme for process disturbances governed by different distributions.
Exploring the role of identity in pro-environmental behavior: cultural and educational influences on younger generations
(2024-10-09) Wild , Steffen; Schulze Heuling, Lydia
It is of paramount importance to gain an understanding of pro-environmental behavior if we are to successfully tackle the climate crisis. The existing body of research provides evidence that identity influences pro-environmental behavior. However, such research is often over-generalised and researchers are challenged to conduct robust analyses with regard to specific local, cultural and educational factors. The present study aims to investigate whether personal or social identity has a distinct effect on three different dimensions of pro-environmental behavior, using the principles of self-categorisation theory. Additionally, the study seeks to determine whether one of these two factors, the individual or the social factor, is predominant over the other. The study group consisted of cooperative students in Germany, typically a group with high professional ambitions. The data was collected in a cross-sectional survey with a total of 568 cooperative students from academic disciplines in engineering and economics. The reliability of the scales is satisfactory (ω = 0.76–0.88), and the hypotheses are tested by estimating structural equation models. Our research demonstrates that while social identity exerts a stronger influence on activist behavior than personal identity, personal identity has a more pronounced effect on consumer behavior than social identity. Nevertheless, no general statement can be made regarding the relative strength of the effects of personal and social identity on pro-environmental behavior dimensions.
Freezing limits for general random matrix ensembles and applications to classical β-ensembles
(2024) Hermann, Kilian; Voit, Michael; Woerner, Jeannette
This thesis studies the asymptotic behavior of eigenvalue distributions in random matrix theory, more specifically that of beta ensembles as the parameter beta tends to infinity. This regime is known as the “freezing limit”. Beta ensembles are often used to describe systems of interacting particles that are influenced by repulsive forces and external potentials. They appear in various physical and mathematical contexts.
In physics, beta ensembles play a key role in Calogero-Moser-Sutherland models. Here, beta represents the inverse temperature, and the freezing limit corresponds to rigid particle configurations. In mathematics, beta ensembles describe eigenvalue densities in classical random matrix models. Examples of such models that are studied in this thesis are the Gaussian, Wishart, and MANOVA ensemble. In the classical sense, the value of beta is fixed and depends on the underlying number field. For arbitrary positive beta, a tridiagonal matrix model can be defined such that its eigenvalue distribution is given by the beta ensemble for this beta.
The thesis focuses first on analyzing the behavior of beta ensembles for general convex potential functions in the freezing limit. These include the classical ensembles, the beta-Hermite, the beta-Laguerre the and beta-Jacobi ensemble as well as certain edge cases. Afterwards, the interplay of the freezing regime and pushing the number of particles to infinity is investigated in each of the three classical cases. These investigations provide new insights into the structural connection between beta ensembles and dual orthogonal polynomial systems.
Self-training for handwritten word recognition and retrieval
(2024) Wolf, Fabian; Fink, Gernot A.; Fornés, Alicia
Over centuries, handwritten documents have been the main mean of capturing and storing information. Libraries and archives have gathered, stored and maintained tremendously large document collections. These collections are in various ways a snapshot of their time and hold incredibly valuable data for social and historical sciences. A significant problem for social scientists and historians alike is that the data stored in this collection is hardly accessible. Usually, no transcriptions exist and the manual creation of them is unfeasible at large scale. This problem motivates the use of automatic systems using techniques such as handwriting recognition or an automatic word search. While these two domains are classic problems considered in the document analysis community and have a long standing tradition, they suffer from a severe drawback. Nowadays, well performing models rely on machine learning techniques, which means models are trained in a supervised fashion using manually annotated training data. The manual creation of training data is a cumbersome process and is the main obstacle that often prevents the application of a automatic document analysis system. This thesis develops a method that allows for the training of handwriting recognition and word spotting models without the need for any manually annotated training samples. The underlying training concept is called self-training and relies on training on automatically generated pseudo-labels.The proposed training scheme can be summarized as follows. First, an initial model is trained on synthetic data that has been generated using a font-based approach. Then, this initial model makes predictions for an unlabeled training data set. Following, the predictions are used for another training step and constitute the current set of pseudo-labels. This process is repeated iteratively, alternating between the prediction of pseudo-labels and training on them. The method is then extended by the integration of a confidence measure that allows for a better selection of less erroneous pseudo-labels. The experiments show that self-training the models considered in this work is feasible and leads to significant performance gains with respect to only training on a synthetic dataset. The investigation of synthetic data generation provides several insights, for example, that training on synthetic data constitutes a form of implicit language modeling, and that a calibrated dataset can be generated by using different style predictor networks. Further experiments on the integration of the confidence measures provide evidence that their use benefits performances and leads to a higher robustness regarding bad performing initial models. It can be concluded that self-training is a highly efficient approach to train well performing models in the absence of manually annotated data and, therefore, provide a potential solution for the application of such models in the data scarce domain of automatic analysis of historical document collections.
Property-based timing analysis of distributed real-time systems
(2024) Günzel, Mario; Chen, Jian-Jia; Baruah, Sanjoy
For real-time systems, timing requirements must be met to avoid catastrophic outcomes. While the behavior of classical real-time systems is already studied extensively in the literature, the trend towards distributed systems raises new challenges. In this dissertation, we focus on the following two challenges: (i) distributed execution of jobs, resulting in self-suspending task behavior, and (ii) interplay of several distributed tasks, requiring to shift the real-time requirements from a single task to a sequence of tasks, the so-called end-to-end latency of cause-effect chains. Although the study of cause-effect chains and self-suspending tasks has led to a series of results, some of them suffer from missing assumptions or use intuitive extension of classical results on real-time systems, resulting in flawed analyses. We tackle this issue by providing careful analysis of self-suspending tasks and cause-effect chains based on fundamental properties of possible evolutions of the system.
The dissertation is structured into five main chapters. In Chapter 2, real-time systems and classical task models used in the literature are introduced. In this dissertation, we pursue a fundamental view on real-time systems, starting from possible system evolutions and schedules, and abstracting task properties afterwards. This is different to the typical procedure of defining the task model first and deriving possible schedules based on the task model. Our approach has the benefit that a task can be observed in different abstraction levels without translating the task into a different task model. Furthermore, in Chapter 2, we introduce scheduling algorithms as a systematic approach to derive task schedules from system evolutions based on the information of the task abstraction, and we discuss analytical literature results for the adherence to real-time requirements.
Chapter 3 introduces the challenges that arise from distributed systems. The first challenge is the distributed execution of jobs. This is enabled by refining tasks into smaller blocks which can be distributed on different computing elements. The impact of this refinement on the generation of schedules is discussed and different refined task models are presented. One of them, the so-called self-suspending task model, is in focus for this dissertation. The second challenge is the interplay of distributed tasks. More specifically, if a functionality is not described by a single task but by a sequence of task (a so-called cause-effect chain) then the timing requirement must be shifted from the single task to the cause-effect chain. The resulting timing metric for cause-effect chains is the end-to-end latency.
Chapter 4 emphasizes the need for careful, property-based analysis. That is, three counterexamples for literature results are provided. Two of them are related to self-suspending tasks, closing the unresolved issues discussed in a review paper on self-suspending tasks in 2019. The third one disproves a basic result for real-time systems in the context of probabilistic setups.
Chapter 5 examines self-suspending tasks. Self-suspending tasks can voluntarily suspend their execution. Such behavior can cause timing anomalies, i.e., the worst-case behavior cannot be observed with maximal execution and suspension time. Therefore, self-suspending tasks require careful analysis and treatment. We provide novel analytical approaches for the Worst-Case Response Time (WCRT) of self-suspending tasks under different scheduling algorithms, namely, (i) Task-level Fixed Priority (T-FP), (ii) Earliest-Deadline-First (EDF) and (iii) EDF-Like (EL), all outperforming the state of the art. Furthermore, we present mechanisms to avoid the analytical pessimism that is necessary to tolerate timing anomalies, namely, segment release time enforcement and segment priority modification.
Chapter 6 examines cause-effect chains. While for typical task models the real-time requirement is given on the task-level, for cause-effect chains the end-to-end latency is considered. We prove fundamental properties of the end-to-end latency, namely the compositional property and the equivalence of typical metrics. Furthermore, we provide novel analyses of the worst-case and probabilistic end-to-end latency. For the worst-case end-to-end latency, we focus on a property-based approach, uncovering fundamental principles of literature results and using our insights from the fundamental properties to derive novel solutions. For the probabilistic end-to-end latency, we are one of the first to define a metric. Therefore, we focus on potential pitfalls and conduct careful analysis.