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Item type:Publication, Access status: with files , Data-driven continuous-time optimal control: a unified framework using orthogonal functionsWe study data-driven optimal control of continuous-time linear systems over finite- and infinite-time horizons. Our approach builds on our continuous-time version of Willems et al.’s fundamental lemma and on the use of orthogonal basis functions to approximate system trajectories. We show that the solution to an optimal control problem can be approximated by a finite linear combination of basis functions and we establish error bounds for such approximations. Moreover, we approximately solve the algebraic Riccati equation and the associated optimal controller gain directly from data, opening up the possibility of optimal controller design directly from data analogue devices.Publicationtype: Journal Article12 20 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , A python toolbox for flexibility aggregation and disaggregation: PyFlexAD(Elsevier, 2025-10-27); ; ; ; The increasing penetration of volatile renewables and growing electricity demand pose several challenges for power systems. Simultaneously, flexible devices – so called distributed energy resources (DER) – are becoming more widespread, making them attractive for providing ancillary services. The flexibility of a single device can be represented by a set of reference power profiles, and the flexibility of multiple devices by the summation of individual flexibility sets. However, set addition, also known as the Minkowski sum, is usually computationally intractable. This has led to the development of various approximation methods in the literature. The current study improves upon our previously published vertex-based inner approximation, by extending it to more general storage devices and hierarchical aggregation settings. We validate the efficacy and accuracy of the proposed method through case studies using real data and provide the source code of the algorithm as a Python package that enables the (dis-)aggregation of various flexible devices in real-world scenarios.Publicationtype: Journal Article39 34 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Towards data-driven multi-stage OPF(IEEE, 2025-06); ; ; ; The operation of large-scale power systems is usually scheduled ahead via numerical optimization. However, this requires models of grid topology, line parameters, and bus specifications. Classic approaches first identify the network topology, i.e., the graph of interconnections and the associated impedances. The power generation schedules are computed by solving a multi-stage optimal power flow (OPF) problem built around the model. In this paper, we explore the prospect of data-driven approaches to multi-stage optimal power flow. Specifically, we leverage recent findings from systems and control to bypass the identification step and to construct the optimization problem directly from data. We illustrate the performance of our method on a 118-bus system and compare it with the classical identification-based approach.Publicationtype: Conference Paper21 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Hidden regularity in singular optimal control of port-Hamiltonian systems(TIB Open Publishing, 2025-01-20); ; ; We study the problem of state transition on a finite time interval with minimal energy supply for linear port-Hamiltonian systems. While the cost functional of minimal energy supply is intrinsic to the port-Hamiltonian structure, the necessary conditions of optimality resulting from Pontryagin's maximum principle may yield singular arcs. The underlying reason is the linear dependence on the control, which makes the problem of determining the optimal control as a function of the state and the adjoint more complicated or even impossible. To resolve this issue, we fully characterize regularity of the (differential-algebraic) optimality system by using the interplay of the cost functional and the dynamics. In case of the optimality DAE being characterized by a regular matrix pencil, we fully determine the control on the singular arc. In case of singular matrix pencils of the optimality system, we propose an approach to compute rank-minimal quadratic perturbations of the objective such that the optimal control problem becomes regular. We illustrate the applicability of our results by a general second-order mechanical system and a discretized boundary-controlled heat equation.Publicationtype: Journal Article9 13 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Distributed optimization for energy grids: a tutorial on ADMM and ALADIN(Institution of Engineering and Technology (IET), 2024-12-17); ; Publicationtype: Book Part46 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , A continuous-time fundamental lemma and its application in data-driven optimal controlData-driven control of discrete-time and continuous-time systems is of tremendous research interest. In this paper, we explore data-driven optimal control of continuous-time linear systems using input–output data. Based on a density result, we rigorously derive error bounds for finite-order polynomial approximations of elements of the system behavior. To this end, we leverage a link between latent variables and flat outputs of controllable systems. Combined with a continuous-time counterpart of Willems et al.’s fundamental lemma, we characterize the suboptimality resulting from polynomial approximations in data-driven linear–quadratic optimal control. Finally, we draw upon a numerical example to illustrate our results.Publicationtype: Journal Article14 40 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Optimal control of port-Hamiltonian systems: energy, entropy, and exergy(Elsevier, 2024-10-26); ; ; ; We consider irreversible and coupled reversible–irreversible nonlinear port-Hamiltonian systems and the respective sets of thermodynamic equilibria. In particular, we are concerned with optimal state transitions and output stabilization on finite-time horizons. We analyze a class of optimal control problems, where the performance functional can be interpreted as a linear combination of energy supply, entropy generation, or exergy supply. Our results establish the integral turnpike property towards the set of thermodynamic equilibria providing a rigorous connection of optimal system trajectories to optimal steady states. Throughout the paper, we illustrate our findings by means of two examples: a network of heat exchangers and a gas-piston system.Publicationtype: Journal Article45 33 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , 31 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Alleviating the curse of dimensionality in minkowski sum approximations of storage flexibilityMany real-world applications require the joint optimization of a large number of flexible devices over time. The flexibility of, e.g., multiple batteries, thermostatically controlled loads, or electric vehicles can be used to support grid operation and to reduce operation costs. Using piecewise constant power values, the flexibility of each device over d time periods can be described as a polytopic subset in power space. The aggregated flexibility is given by the Minkowski sum of these polytopes. As the computation of Minkowski sums is in general demanding, several approximations have been proposed in the literature. Yet, their application potential is often objective-dependent and limited by the curse of dimensionality. We show that up to 2d vertices of each polytope can be computed efficiently and that the convex hull of their sums provides a computationally efficient inner approximation of the Minkowski sum. Via an extensive simulation study, we illustrate that our approach outperforms ten state-of-the-art inner approximations in terms of computational complexity and accuracy for different objectives. Moreover, we propose an efficient disaggregation method applicable to any vertex-based approximation. The proposed methods provide an efficient means to aggregate and to disaggregate energy storages in quarter-hourly periods over an entire day with reasonable accuracy for aggregated cost and for peak power optimization.Publicationtype: Journal Article27 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Behavioral theory for stochastic systems? A data-driven journey from Willems to Wiener and back againThe fundamental lemma by Jan C. Willems and co-workers is deeply rooted in behavioral systems theory and it has become one of the supporting pillars of the recent progress on data-driven control and system analysis. This tutorial-style paper combines recent insights into stochastic and descriptor-system formulations of the lemma to further extend and broaden the formal basis for behavioral theory of stochastic linear systems. We show that series expansions – in particular Polynomial Chaos Expansions (PCE) of L2-random variables, which date back to Norbert Wiener's seminal work – enable equivalent behavioral characterizations of linear stochastic systems. Specifically, we prove that under mild assumptions the behavior of the dynamics of the L2-random variables is equivalent to the behavior of the dynamics of the series expansion coefficients and that it entails the behavior composed of sampled realization trajectories. We also illustrate the short-comings of the behavior associated to the time-evolution of the statistical moments. The paper culminates in the formulation of the stochastic fundamental lemma for linear time-invariant systems, which in turn enables numerically tractable formulations of data-driven stochastic optimal control combining Hankel matrices in realization data (i.e. in measurements) with PCE concepts.Publicationtype: Journal ArticleScopus© Citations 8 11 251