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    FOR 5785: Benchmarks für aktive Lernverfahren in der Systemtheorie und Regelungstechnik
    As part of the research unit "Active Learning for Systems and Control (ALeSCo) - Data Informativity, Uncertainty, and Guarantees", this project investigates benchmarks for active learning in systems and control. Evaluation and benchmarks are crucial for the transparent comparison of methods across various fields, including machine learning, optimization, and control systems. While datasets and test problems exist for supervised learning, different branches of control, and robotics, a notable gap exists in benchmarks focused on active learning for dynamic systems. This project aims to address and bridge this gap by developing representative and challenging scenarios to evaluate and compare active learning techniques for systems and control. We propose regression subtasks and closed-loop evaluation procedures equipped with tailored assessment metrics. Specifically, we consider multi-energy systems and robotics as application domains. We create scalable test problems for multi-energy distribution systems, integrating real-world datasets as well as 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. It will allow to evaluate active learning tasks to improve control schemes under stochastic disturbances and parametric drifts as well as uncertain network topology. In the robotics domain, we introduce benchmarks for autonomous navigation and manipulation tasks for unmanned underwater vehicle and soft robotic arm models. These benchmarks will consider kinematics, dynamics, and environmental disturbances with adjustable levels of system complexity in terms of state and input dimensions as well as availability of information about model parameters and system states. Experimentally derived sensor noise and external disturbance models will help to reduce the gap between simulation and reality. The benchmarks facilitate transparent method comparison through a multi-dimensional metric framework, including classical concepts such as learning rates, safety violations, computation times, and regret measures. A core research question of this project is how control-theoretic concepts like data informativity, invariance, and stability can translate to metrics for algorithm evaluation. The benchmark will be open-source, adhere to the FAIR principles, and will offer a Python API, ensuring interoperability with existing machine-learning environments. By modular and customizable design, we aim to accelerate research within and beyond the ALeSCo consortium and provide researchers the flexibility to adapt to emerging tasks. In summary, the project aims to provide a framework for evaluating active learning methods, pushing existing algorithms to their limits, and establishing a foundation for future research and innovations in multi-energy systems and robotics.
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    Linking Approximate Dynamic Programming, Predictive Control, and Dissipativity: Novel Adaptive Control Approaches for Nonlinear Systems
    Approximate Dynamic Programming (ADP), Model Predictive Control (MPC), and dissipativity are established concepts, which are closely related through optimality considerations. Indeed, there is mature understanding of many aspects of MPC such as, e.g., nominal stability and performance. Beyond nominal considerations, robust designs are often intrinsically conservative and stochastic methods tend to induce a substantial mathematical overhead. Hence, in the face of uncertainty, control approaches for nonlinear systems which allow for online adaptation of models, feedback laws, or both are of growing interest. In the context of MPC, ADP concepts are promising guiding principles for online adaptation due to their close mutual relation. Yet, established analysis techniques for MPC often use upper-bounds on the cost-to-go (e.g. in tracking MPC with terminal ingredients) or they rely on lower-bounds on the cost-to-go (e.g. in dissipativity-based designs). Conceptually, we aim to broaden the scope, i.e., we consider terminal penalties that are mere approximations of the cost-to-go. Specifically, this project explores new approaches to adaptive control of nonlinear systems linking ADP, MPC, and dissipativity. We focus on two fundamental research questions: i) How to leverage ADP for the design of MPC controllers for nonlinear systems subject to model uncertainty? ii) How to exploit dissipativity concepts in ADP? The investigations with respect to i) target the understanding of model uncertainty in ADP and the analysis of approximations errors of ADP. For this, we investigate the interplay of closed-loop stability and approximation errors and the effect of model errors on ADP control policies. In turn, these considerations provide the basis to analyze the robustness of MPC wherein the terminal penalty is not an upper-bound on the cost-to-go but a mere approximation of it. Moreover, we are interested in analyzing the closed-loop performance of MPC with approximated cost-to-go. At the core of our investigations of ii) is the deep relation between optimal control and the dissipativity notion of open systems. Specifically, we leverage the links between storage functions needed for dissipativity and infinite-horizon value functions of optimal control problems to develop novel schemes for dissipativity-informed online ADP. The helpful relations between storage and value functions include gradient approximation properties and the fact that the storage provides a lower bound on the value function. Moreover, we combine the insights of our investigations on i) with the above towards dissipativity-informed online adaptation in MPC. Our findings are validated on case studies from biogas reactors, which is subject to growing research attention due to the increasing need for renewable energy sources.
      14
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    FOR 5785: Neural ODE training via stochastic control and uncertainty quantification
    This project is part of the research unit "Active Learning for Systems and Control (ALeSCo) - Data Informativity, Uncertainty, and Guarantees". 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, in particular concepts from uncertainty quantification and stochastic control, can be beneficial in the design and analysis of training formulations for neural networks. Specifically, the project considers Neural Ordinary Differential Equations (NODEs) and their explicit discretizations which take the form of Residual Networks (ResNets). We formulate and analyze the propagation of data through NODEs and ResNets in the framework of Polynomial Chaos Expansions (PCE) of L2 random variables, a concept proposed by Norbert Wiener. These random variables are used to model the input data of neural networks, which enables the forward propagation of entire sets of input data. Using the PCE description of the propagated data in the output layer, we explore the analysis of generalization properties. We extend the uncertainty propagation towards the training of NODEs and ResNets combining the PCE-based L2 framework with optimal control formulations of the training problem. 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. Moreover, we devise active learning strategies based on the conceived L2 training problems. Specifically, we investigate how the propagated input data enables uncertainty quantification for label predictions. 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.
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    CRC 1615 - Project C05: Adaptive and Learning-based Control Architectures for SMART Reactors
    Reactors of the future need to be “SMART”: Sustainable, Multipurpose, Autonomous (self-adaptive), Resilient, and Transferable. Control and process engineering leveraging learning, feedback, and online adaptation are pivotal in bringing forth these attributes: Modern optimization-based process control fosters sustainability as it enables to optimize process performance while satisfying operational constraints. 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. Put differently, feedback control is indispensable for realizing the SMART attributes in reactor operation.On this canvas, this project investigates tailored control methods for SMART reactors. We consider 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 first question is approached through a hybrid modelling strategy, wherein first-principles models are combined with reaction and process specific data-driven model components. In this context, a key tool are data-driven models based on composite reproducing kernel structures which allow for flexible system description capturing different use cases. We then use these models in optimization-based and predictive control schemes.For the second question, we consider a Bayesian approach to real-time optimization for SMART reactors. In particular, we explore the use of safe variants of Wiener kernel regression for a real-time optimization of process performance. We investigate how to combine existing first-principles models with correction terms obtained from kernel regression – with and without distributional uncertainty surrounding the additive measurement disturbance. Eventually, this leads to the consideration of risk measures in the objective of the real-time optimization.The developed methods are tested on the van de Vusse scheme before we consider other reactions investigated in project areas B and C of the CRC.
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    TRR 391 Teilprojekt B03: Statistical methods for energy systems: aggregation and decomposition
    Statistische Methoden für Energiesysteme: Aggregation und Dekomposition befasst sich mit statistischen Methoden der Aggregation und Dekomposition von Energieverteilnetzen, um deren Komplexität aus der Perspektive der übergeordneten Übertragungsnetze beherrschbar zu machen. Langfristig werden Methoden für Energieverteilnetze entwickelt, die Multi-Energie-Aspekte einschließlich Fernwärme-, Heizungs-, Lüftungs- und Klimatisierungssystemen abdecken.
      7
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    Exploiting nonlinear port-Hamiltonian structures for optimization-based and data-driven control
    Port-Hamiltonian (pH) systems are ubiquitous in engineering. Application domains encompass mechanics, electrical circuits, thermodynamics, and multi-energy systems to name but a few. Key advantages of the pH perspective are balance equations for physical quantities like energy and entropy, and closedness of pH systems under power-conserving interconnections. This project concerns optimal control of nonlinear port-Hamiltonian systems. We consider dissipative, reversible, and irreversible pH systems and we investigate physically-motivated optimal control problems (OCPs), e.g., state transition with minimal energy supply and/or entropy growth. We exploit the port-Hamiltonian structure intertwined in dynamics and cost functions to thoroughly analyze and to efficiently solve such OCPs. To this end, we proceed in three main steps. First, we analyze port-Hamiltonian OCPs using dissipativity-based methods invoking the nonlinear balance equations for energy and entropy. Furthermore, we consider multi-objective OCPs in view of minimizing the supplied energy and the generated entropy while simultaneously maximizing a produced quantity of interest. Finally, we broaden the analysis towards optimal control of cyclo-passive port-Hamiltonian systems. Second, we tailor Newton homotopy methods to solve the intrinsically-motivated but singular port-Hamiltonian OCPs. To this end, we approximate the solution by a sequence of regularized problems. Further, we construct preconditioners consistent with the pH structure to efficiently conduct the Newton step. Third, we propose novel variants of SINDy (Sparse Identification of Nonlinear Dynamics) and eDMD (extended Dynamic Mode Decomposition) tailored to nonlinear pH systems: On the one hand, we aim to reduce data requirements by leveraging the pH structures. On the other hand, we ensure that key quantities, e.g., the energy balance, are properly taken into account in the data-driven surrogate models while providing rigorous bounds on the approximation error. In conclusion, we analyze physically-motivated OCPs of pH systems and their numerical solution. We develop novel algorithms to efficiently control nonlinear pH systems, e.g., w.r.t. the required energy supply or data requirements, while providing guarantees on stability, numerical efficiency, and approximation accuracy of data-driven surrogate models.
      12
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    Rethinking Cooperation in Distributed MPC: The Anticipation, the Reduction, and the Scaling of Consensus Constraints
    Model Predictive Control (MPC) has had substantial impact on industrial control practice in several industrial domains. However, when it comes to distributed cooperative settings, where large-scale networks comprised of dynamic subsystems are to be controlled in multi-agent fashion, its application still faces substantial challenges. Indeed, distributed predictive control requires the reconciliation of performance, communication, and coordination in different dimensions: problem formulation, system-theoretic analysis, and tailored decentralized optimization algorithms. In distributed MPC the cooperation among subsystems is achieved and fostered through consensus about the taken control actions, which is expressed through specific constraints. However, the convergence of the underlying numerical optimization is often slowed down by the need for consensus, i.e., the consensus constraints induce the need for the communication of optimization iterates between the controllers of the individual subsystems. On this canvas, this project rethinks cooperation in distributed MPC from the consensus point of view. That is, we explore new avenues to leverage the anticipation, the reduction, and the scaling of consensus constraints in the design, the system-theoretic analysis, and the algorithmic implementation of distributed cooperative predictive control. Specifically, we develop new methods for the scalable distributed anticipation of the dual variables of the consensus constraints and for the efficient use of these dual predictions in tailored numerical algorithms. Moreover, we investigate the effect of reducing the consensus constraint in time, i.e., instead of requiring consensus to hold over the entire prediction horizon we develop a new framework for closed-loop analysis with a consensus horizon shorter than the prediction horizon. Finally, we also research novel numerical methods for the scaling and the reduction of the consensus constraints, i.e., we create schemes for the distributed computation of pre-conditioners of the consensus constraints and for the dimensionality reduction of the consensus constraints in the dual space. Our findings are validated on case studies from mechatronics and energy systems.
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