Direct Air Capture is a promising carbon dioxide removal technology, offering safe, flexible, and scalable negative emissions. However, the capture costs and productivity of the Direct Air Capture process are highly influenced by fluctuations in weather conditions, such as ambient temperature and humidity, which hinder its large-scale adoption. Thus, in order to commercialize Direct Air Capture, it is vital to design a control method that reduces the capture costs and enhances productivity while considering the effects of local climate conditions. Due to the complexity of the coupled thermodynamic, heat, and mass transfer phenomena at the core of Direct Air Capture, the unavailability of a sufficiently efficient model, the intractability of parameter estimation, and the high computational costs of model-based approaches, we propose a model-free and data-driven rule-based control approach to improve the performance of Direct Air Capture and reduce its costs. The proposed rule-based control strategy functions as an online policy, continuously receiving feedback from ambient temperature and humidity, enabling dynamic adjustments. Therefore, to maximize the overall system performance, we need to obtain the optimal control law within the considered class of rule-based control schemes. To this end, we utilize a Bayesian optimization framework to optimally tune the parameters of the rule-based control strategy, leveraging data from the online operation influenced by climate conditions. We demonstrate that the proposed method increases the annual Direct Air Capture productivity by up to 16.7 % and lowers the annual capture costs by up to 10.3 % relative to the baseline method. We also observe that the proposed method achieves an annual productivity improvement of 13.59 % and an annual cost reduction of 9.30 % relative to the baseline in Amsterdam, outperforming a data-enabled predictive control method, which achieves 7.07 % productivity improvement and 8.25 % cost reduction, and a reinforcement learning-based controller, which achieves 3.63 % productivity improvement and 3.12 % cost reduction.

Manufacturing productivity demands positioning systems that achieve both high speed and micrometer-level accuracy. Existing approaches rely on time-intensive manual tuning or optimize controller layers independently. We extend prior work on data-driven controller tuning to demonstrate that jointly optimizing Model Predictive Contouring Control (MPCC) planner parameters and low-level controller gains using constrained Bayesian optimization improves performance beyond sequential or isolated tuning strategies. The approach models system performance metrics such as traversal time, tracking accuracy, and vibration levels over complete geometric trajectories as joint Gaussian processes, enabling sample-efficient exploration of the combined parameter space while respecting physical constraints. Numerical results show that joint optimization achieves 8–23% improvement in traversal time and 2.5 - 5 × reduction in maximum contour errors compared to optimizing either layer independently. Experimental validation on precision motion hardware demonstrates that MPCC parameter optimization alone (with pre-tuned low-level gains) achieves 15% improved maximal tracking error at a 6% faster traversal time. The framework is system-agnostic and requires no hardware modifications.

This paper presents a unified and systematic study of compact Transformer architectures for time series forecasting. We introduce a modular framework that standardizes three widely used Transformer families—Autoformer, Informer, and PatchTST—into three principled architectural variants: Minimal, Standard, and Full, enabling controlled analysis of model capacity, inductive bias, and computational complexity. For each family, we provide consistent mathematical formulations, layer-wise descriptions, and end-to-end complexity characterizations. We conduct over 1500 controlled experiments on ten synthetic time series under varying patch lengths, forecast horizons, and noise levels. The results reveal clear and reproducible performance regimes: PatchTST Standard achieves the best overall accuracy and noise robustness, Autoformer variants excel on smooth and trend-dominated signals, and Informer variants exhibit sensitivity to noise and long horizons despite improved scalability. Complementing the empirical analysis, we derive new theoretical results that quantify noise attenuation, bias–variance trade-offs, and approximation–complexity guarantees specific to each architectural family. Finally, we demonstrate that these compact Transformer variants serve as effective and interpretable temporal encoders within an operator–theoretic forecasting framework. By embedding Autoformer, Informer, and PatchTST backbones into a Koopman-based latent dynamics model, we extend their applicability beyond synthetic benchmarks to real-world climate, cryptocurrency and electricity generation time series. Together, these results position compact, modular Transformers as scalable and theoretically grounded building blocks for scientific time series forecasting.

We present a continuous modelling framework for simulating the dynamics of metabolic-regulatory networks (MRNs), designed to overcome the scalability limitations of traditional hybrid models. Hybrid approaches, often based on Boolean logic to represent regulatory interactions, become computationally intractable as the number of regulatory proteins increases, due to an exponential growth in discrete modes and transitions. To address this, our framework replaces discrete logic with smooth Hill functions, enabling the approximation of switch-like regulatory behaviour without introducing combinatorial complexity. This continuous formulation maintains the biological interpretability of hybrid models while greatly enhancing computational efficiency. Parameter estimation, a common bottleneck in continuous models, is simplified in our approach by requiring fewer kinetic parameters than typical hybrid models. We further employ sparse-based system identification, a data-driven technique that efficiently infers network dynamics by selecting a minimal set of nonlinear terms. This method avoids exhaustive search procedures and yields interpretable kinetic models. Applied to MRNs, our framework demonstrates the ability to capture essential regulatory mechanisms with reduced complexity and improved scalability.

We propose a data-driven, user-centric vehicle-to-grid (V2G) methodology based on multi-objective optimization to balance battery degradation and V2G revenue according to EV user preference. Given the lack of accurate and generalizable battery degradation models, we leverage input convex neural networks (ICNNs) to develop a data-driven degradation model trained on extensive experimental datasets. This approach enables our model to capture nonconvex dependencies on battery temperature and time while maintaining convexity with respect to the charging rate. Such a partial convexity property ensures that the second stage of our methodology remains computationally efficient. In the second stage, we integrate our data-driven degradation model into a multi-objective optimization framework to generate an optimal smart charging profile for each EV. This profile effectively balances the trade-off between financial benefits from V2G participation and battery degradation, controlled by a hyperparameter reflecting the user prioritization of battery health. Numerical simulations show the high accuracy of the ICNN model in predicting battery degradation for unseen data. Finally, we present a trade-off curve illustrating financial benefits from V2G versus losses from battery health degradation based on user preferences and showcase smart charging strategies under realistic scenarios.

This article introduces output prediction methods for two types of systems containing sinusoidal-input uniformly convergent (SIUC) elements. The first method considers these elements in combination with single-input single-output linear time-invariant (LTI) systems before, after, and in parallel to them. The second method considers a multiple-input multiple-output LTI system where each input is controlled by an SIUC element. The output prediction only requires frequency-response functions of the LTI elements and is fully accurate for sinusoidal inputs.

Achieving the Paris Agreement's goal necessitates not only reducing carbon dioxide emissions to net zero but also actively removing CO₂ from the atmosphere. Direct Air Capture (DAC) emerges as a pivotal technology in this effort, offering a reliable, flexible, and scalable solution for negative emissions. However, DAC performance is highly sensitive to environmental factors such as temperature and humidity. Consequently, it is vital to develop dynamic control and optimization mechanisms that can enhance the cost-efficiency of DAC. Due to the complexity and lack of a comprehensive model for DAC systems, the need for expert knowledge for modeling, and high computational costs, traditional model-based methods are not feasible. Therefore, we suggest a model-free, data-driven optimization technique based on Bayesian optimization to enhance the productivity and cost-effectiveness of DAC.

Dynamic Programming suffers from the curse of dimensionality due to large state and action spaces, a challenge further compounded by uncertainties in the environment. To mitigate these issue, we explore an off-policy based Temporal Difference Approximate Dynamic Programming approach that preserves contraction mapping when projecting the problem into a subspace of selected features, accounting for the probability distribution of the perturbed transition probability matrix. We further demonstrate how this Approximate Dynamic Programming approach can be implemented as a particular variant of the Temporal Difference learning algorithm, adapted for handling perturbations. To validate our theoretical findings, we provide a numerical example using a Markov Decision Process corresponding to a resource allocation problem.

District heating networks (DHNs) are essential in providing efficient heating services to urban areas through networked pipes. The performance of these systems critically depends on the strategic placement of thermal storage buffers (actuators) and temperature sensors throughout the network. Due to the inherent slow dynamics of thermal transport, these systems exhibit significant delays and periodic behaviors that necessitate time-varying analysis approaches. This paper presents a frequency-domain framework for optimal actuator and sensor placement in DHNs, focusing on metrics derived from frequential Gramians. We provide rigorous analysis of two key metrics, namely the trace and log-determinant of the frequential Gramian, establishing submodularity properties and performance guarantees for greedy selection algorithms. Our theoretical framework naturally handles both the periodic nature of DHNs and their slow transients, outperforming standard approaches in estimation accuracy.

In this article, we propose an economic nonlinear model predictive control (MPC) algorithm for district heating networks (DHNs). The proposed method features prosumers, multiple producers, and storage systems, which are essential components of 4th-generation DHNs. These networks are characterized by their ability to optimize their operations, aiming to reduce supply temperatures, accommodate distributed heat sources, and leverage the flexibility provided by thermal inertia and storage—each crucial for achieving a fossil-fuel-free energy supply. Developing a smart energy management system to accomplish these goals requires detailed models of highly complex nonlinear systems and computational algorithms able to handle large-scale optimization problems. To address this, we introduce a graph-based optimization-oriented model that efficiently integrates distributed producers, prosumers, storage buffers, and bidirectional pipe flows, such that it can be implemented in a real-time MPC setting. Furthermore, we conducted several numerical experiments to evaluate the performance of the proposed algorithms in closed loop. Our findings demonstrate that the MPC methods achieved up to 9% cost improvement over traditional rule-based controllers while better maintaining system constraints.

This article presents the guided Bayesian optimization (BO) algorithm as an efficient data-driven method for iteratively tuning closed-loop controller parameters using a digital twin of the system. The digital twin is built using closed-loop data acquired during standard BO iterations, and activated when the uncertainty in the Gaussian Process model of the optimization objective on the real system is high. We define a controller tuning framework independent of the controller or the plant structure. Our proposed methodology is model-free, making it suitable for nonlinear and unmodelled plants with measurement noise. The objective function consists of performance metrics modeled by Gaussian processes. We utilize the available information in the closed-loop system to progressively maintain a digital twin that guides the optimizer, improving the data efficiency of our method. Switching the digital twin on and off is triggered by our data-driven criteria related to the digital twin’s uncertainty estimations in the BO tuning framework. Effectively, it replaces much of the exploration of the real system with exploration performed on the digital twin. We analyze the properties of our method in simulation and demonstrate its performance on two real closed-loop systems with different plant and controller structures. The experimental results show that our method requires fewer experiments on the physical plant than Bayesian optimization to find the optimal controller parameters.

In this paper, we present an impulse response identification scheme that incorporates the internal positivity side-information of the system. The realization theory of positive systems establishes specific criteria for the existence of a positive realization for a given transfer function. These transfer function criteria are translated to a set of suitable conditions on the shape and structure of the impulse responses of positive systems. Utilizing these conditions, the impulse response estimation problem is formulated as a constrained optimization in a reproducing kernel Hilbert space equipped with a stable kernel, and suitable constraints are imposed to encode the internal positivity side-information. The optimization problem is infinite-dimensional with an infinite number of constraints. An equivalent finite-dimensional convex optimization in the form of a convex quadratic program is derived. The resulting equivalent reformulation makes the proposed approach suitable for numerical simulation and practical implementation. A Monte Carlo numerical experiment evaluates the impact of incorporating the internal positivity side-information in the proposed identification scheme. The effectiveness of the proposed method is demonstrated using data from a heating system experiment.

The inherently nonlinear, large-scale, and time-varying nature of district heating systems pose significant challenges from a control perspective. In this paper, we address these challenges by applying an economic MPC. Economic MPC is a dynamic real-time optimization method, enabling both optimal planning and stability of the closed-loop system. Our strategy constitutes several steps. First, we introduce a discrete-time modular framework for the district heating system, establishing its strict dissipativity with respect to a desired, potentially time-varying, equilibrium. We identify a set of meaningful objective functions for the district heating systems, preserving this property. Second, we show how strict dissipativity implies the turnpike property, which, in turn, guarantees approximate optimality, practical stability, and recursive feasibility for the EMPC closed-loop. Finally, we provide numerical simulations to demonstrate the effectiveness of our work.

Model Predictive Control can cope with conflicting control objectives in building energy managements. In terms of user satisfaction, visual comfort has been proven in several studies to be a crucial factor, however thermal comfort is typically considered the only important aspect. Besides human well-being, visual comfort strongly impacts the productivity of the occupants in offices. Therefore, from an economic point of view, it is essential to include visual comfort in Model Predictive Control for buildings. In this paper semi-linear support vector machine is applied to learn suitable models for visual comfort measured by Daylight Glare Probability. The resulting model is incorporated into a Model Predictive Control framework, together with an autoregressive exogenous model accounting for the thermal dynamics of the building. The approach is validated through an extensive numerical case study, and the benefits of including visual comfort and blind control in the Model Predictive Control problem are evaluated. We observe that the proposed Model Predictive Control scheme ensures both the thermal and visual comfort constraints at the expense of 2.2% to 7.2% higher energy consumption compared to the benchmark Model Predictive Control configuration, which considers only the thermal comfort constraints.

In this paper, we discuss the learning and discovery problem for the dynamical systems described through stable evolutionary Partial Differential Equations (PDEs). The main idea is to employ a suitable learning approach for creating a map from boundary conditions to the corresponding output. More precisely, in order to accurately uncover the evolutionary PDE dynamics, we propose a scheme that employs large-scale system identification to construct such a map using sufficiently informative measurements. Accordingly, we first develop a scalable implementation for the subspace identification method, enforcing stability on the identified system. To this end, numerical optimization techniques such as coordinate descent, randomized singular value decomposition, and large-scale semidefinite programming are employed. The performance and complexity of the resulting scheme are discussed and demonstrated through numerical experiments on generic identification examples. Following this, we validate the effectiveness of the proposed approach on an example of a stable evolutionary partial differential equation. The numerical results confirm the efficacy of the proposed learning scheme.

We study the problem of identifying a linear time-varying output map from measurements and linear time-varying system states, which are perturbed with Gaussian observation noise and process uncertainty, respectively. Employing a stochastic model as prior knowledge for the parameters of the unknown output map, we reconstruct their estimates from input/output pairs via a Bayesian approach to optimize the posterior probability density of the output map parameters. The resulting problem is a non-convex optimization, for which we propose a tractable linear matrix inequalities approximation to warm-start a first-order subsequent method. The efficacy of our algorithm is shown experimentally against classical Expectation Maximization and Dual Kalman Smoother approaches.

In this work, we consider the problem of learning the Koopman operator for discrete-time autonomous systems. The learning problem is formulated as a generic constrained regularized empirical loss minimization in the infinite-dimensional space of linear operators. We show that a representer theorem holds for the introduced learning problem under certain but general conditions, which allows convex reformulation of the problem in a specific finite-dimensional space without any approximation and loss of precision. We discuss the inclusion of various forms of regularization and constraints in the learning problem, such as the operator norm, the Frobenius norm, the operator rank, the nuclear norm, and the stability. Subsequently, we derive the corresponding equivalent finite-dimensional problem. Furthermore, we demonstrate the connection between the proposed formulation and the extended dynamic mode decomposition. We present several numerical examples to illustrate the theoretical results and verify the performance of regularized learning of the Koopman operators.