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 article addresses the control of large-scale district heating networks (DHNs). Traditional nonlinear model predictive control (MPC) suffers from computational intractability due to the nonconvex optimization of complex thermal-hydraulic dynamics. We present scalable predictive control strategies based on the Koopman operator framework, developing a physics-guided methodology to construct meaningful Koopman observables by integrating the network’s graph topology and thermodynamic conservation laws. This ensures that critical nonlinear interactions and energy transport phenomena are accurately captured in physically interpretable lifted representations. The resulting linear model enables a Koopman-based receding horizon formulation in which each iteration reduces to a convex quadratic program (QP), guaranteeing global optimality of the QP surrogate at each step. Extensive numerical validation on benchmark DHNs demonstrates computational speedups exceeding one order of magnitude over state-of-the-art nonlinear MPC while maintaining comparable control performance. We further extend the methodology to DHNs with bidirectional-flow pipes, providing a tractable optimization framework with superior performance compared to nonlinear MPC.

Nonlinear systems can be lifted to higher-dimensional spaces where their dynamics evolve linearly, enabling linear analysis and control. However, most existing approaches prioritize the linearity of the lifted dynamics and accurate state reconstruction, while overlooking whether the features of interest are actually observable from the measured outputs. To address this limitation, we propose an observability-aware Koopman lifting framework that incorporates a short-horizon observability check alongside standard invariance and reconstruction objectives. The formulation separates roles by employing a linear output map for identifiability and a nonlinear reconstruction map for high-fidelity recovery. Rather than verifying observability post hoc, the proposed method embeds it directly into the training objective to actively shape the learned model. Experiments on benchmark nonlinear systems, namely the Van der Pol and Duffing oscillators, demonstrate that the proposed approach yields better-conditioned lifted-to-output mappings, stronger identifiability, and a more reliable spectral profile than invariance-only and fixed-dictionary baselines, while revealing a trade-off in long-horizon rollout accuracy.

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.

This paper presents a novel data-driven Reference Governor with Model Predictive Control, integrating local motion replanning and path following for collision avoidance. Employing a model-free Reference Governor, the proposed framework utilises system knowledge through Bayesian Optimisation to augment predetermined evasive trajectories, minimising pathfollowing errors and simultaneously ensuring obstacle safety margins. A single-track vehicle model in combination with a nonlinear tyre model is used to capture the vehicle's dynamics. The optimised control action is the vehicle steering angle, whilst the Reference Governor optimises parameters of a sigmoid reference signal to minimise the tracking error and guarantee safety with respect to obstacles in emergency manoeuvres. The proposed approach is evaluated on a single lane change using a highfidelity simulation environment, and its performance is compared to a baseline controller integrating path following and obstacle avoidance. The results demonstrate a 14% reduction in safety critical overshoot, maximising obstacle safety distance and a four times lower controller cycle time compared to the baseline. Furthermore, through a robustness analysis, it is demonstrated that the proposed approach is more robust towards model mismatches and perception-based errors, as seen by average 30% and 40% reductions in near-miss and collision rates.

Human memory consolidation involves the gradual stabilization and reorganization of memory traces over time. Despite numerous empirical and computational accounts emphasizing different aspects of this process, an integrated framework for evaluating consolidation theories against brain data remains limited. We propose a biologically informed, data-driven framework based on Koopman operator analysis to examine latent dynamical structure in fMRI signals associated with memory consolidation. The Koopman framework lifts nonlinear brain dynamics into a linear function space, enabling spectral characterization of persistence and stability. In practice, we employ Dynamic Mode Decomposition (DMD) together with an observability-aware extension tailored to consolidation-related neural dynamics. We organize existing theories into three functional clusters: standard consolidation, episodic replay during rest, and distributed long-term storage, and then align open-access fMRI datasets with each cluster to assess their dynamical plausibility. Across datasets, delayed or repeated retrieval conditions generally tend to show greater spectral persistence than early encoding-related conditions. Among the three analyses, Cluster 3 yielded the clearest statistically reliable subject-level contrast, with semantically abstracted autobiographical content exhibiting higher mean eigenvalue magnitude and more near-unit modes than event-specific episodic content. This finding is compatible with transformation-oriented and distributed-storage accounts but does not constitute a direct temporal test of consolidation. Replay-related conditions show strong spectral differentiation across task states, although part of this separation likely reflects task structure in addition to consolidation-related dynamics. For the standard consolidation cluster, effects are directionally consistent with theory but remain small and not statistically significant at the subject level. Overall, the proposed framework provides an interpretable operator-theoretic approach for linking memory consolidation theory to latent brain dynamics and for comparing competing accounts in a common spectral language.

Assuming access to prior knowledge about the unknown system parameter θ, given as a probability prior ϕ(θ), we study how such information can be incorporated into the adaptive control design of nonlinear systems. To this end, we propose a new parameter estimation law, and show that it pro-motes convergence of parameter estimates to high-probability regions of the parameter space. Our approach is particularly useful when employed as a single universal controller for a large population of systems with similar dynamic structure but different parameter values. In this scenario, our method, on average, leads to a more accurate parameter estimate, which consequently improves transient performance and accelerates state convergence. Numerical studies confirm the effectiveness of the proposed method.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.