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W. P. M. H. Heemels

Publications and source records attributed to W. P. M. H. Heemels.

At least 19 recordsLinked to original sources
arXiv2026

Overlapping Covariance Intersection: Fusion with Partial Structural Knowledge of Correlation from Multiple Sources

Emerging large-scale engineering systems rely on distributed fusion for situational awareness, where agents combine noisy local sensor measurements with exchanged information to obtain fused estimates. However, at the sheer scale of these systems, tracking cross-correlations becomes infeasible, preventing the use of optimal filters. Covariance intersection (CI) methods address fusion problems with unknown correlations by minimizing worst-case uncertainty based on available information. Existing CI extensions exploit limited correlation knowledge but cannot incorporate structural knowledge of correlation from multiple sources, which naturally arises in distributed fusion problems. This paper introduces Overlapping Covariance Intersection (OCI), a generalized CI framework that accommodates this novel information structure. We formalize the OCI problem and establish necessary and sufficient conditions for feasibility. We show that a family-optimal solution can be computed efficiently via semidefinite programming, enabling real-time implementation. The proposed tools enable improved fusion performance for large-scale systems while retaining robustness to unknown correlations.

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arXiv2026

Token Economy Design for Fair and Efficient Highway Congestion Management with Express Lanes

We study the design of a token economy for highway lane allocation that aims to improve fairness without sacrificing traffic efficiency. Motivated by the San Mateo 101 Express Lanes Project, we consider a setting in which high-occupancy vehicles have unrestricted access to an express lane, while the remaining users can alternate between regular and express lanes by earning and spending nonmonetary tokens. We model the resulting interaction as a finite-population dynamic congestion game with heterogeneous time preferences and limited-information evolutionary policy revisions. Building on a mean-field approximation, we derive token prices that enforce the system-optimal lane split while inducing fairness over time through turn-taking. The scheme is evaluated in a microscopic traffic simulation with real-world demand data. The results show that the proposed prices yield nearly the same average travel time as a baseline scenario in which no lane is reserved as an express lane, while substantially reducing urgency-weighted perceived travel time. These findings highlight token economies as a promising alternative to monetary congestion pricing for fairer management of scarce road capacity.

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arXiv2026

A Unified Family-optimal Solution to Covariance Intersection Problems with Semidefinite Programming

Covariance intersection (CI) methods provide a principled approach to fusing estimates with unknown cross-correlations by minimizing a worst-case measure of uncertainty that is consistent with the available information. This paper shows that a generalized CI framework, called overlapping covariance intersection (OCI), unifies several existing CI formulations within a single optimization-based framework. This unification enables the characterization of family-optimal solutions for multiple CI variants, including standard CI and split covariance intersection (SCI), as solutions to a semidefinite program, for which efficient off-the-shelf solvers are available. When specialized to the corresponding settings, the proposed family-optimal solutions recover the state-of-the-art family-optimal solutions previously reported for CI and SCI. The resulting formulation facilitates the systematic design and real-time implementation of CI-based fusion methods in large-scale distributed estimation problems, such as cooperative localization.

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arXiv2026

Data-Driven Stabilization Using Prior Knowledge on Stabilizability and Controllability

In this work, we study data-driven stabilization of linear time-invariant systems using prior knowledge of system-theoretic properties, specifically stabilizability and controllability. To formalize this, we extend the concept of data informativity by requiring the existence of a controller that stabilizes all systems consistent with the data and the prior knowledge. We show that if the system is controllable, then incorporating this as prior knowledge does not relax the conditions required for data-driven stabilization. Remarkably, however, we show that if the system is stabilizable, then using this as prior knowledge leads to necessary and sufficient conditions that are weaker than those for data-driven stabilization without prior knowledge. In other words, data-driven stabilization is easier if one knows that the underlying system is stabilizable. We also provide new data-driven control design methods in terms of linear matrix inequalities that complement the conditions for informativity.

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arXiv2026

Data-Efficient Quadratic Q-Learning Using LMIs

Reinforcement learning (RL) has seen significant research and application results but often requires large amounts of training data. This paper proposes two data-efficient off-policy RL methods that use parametrized Q-learning. In these methods, the Q-function is chosen to be linear in the parameters and quadratic in selected basis functions in the state and control deviations from a base policy. A cost penalizing the $\ell_1$-norm of Bellman errors is minimized. We propose two methods: Linear Matrix Inequality Q-Learning (LMI-QL) and its iterative variant (LMI-QLi), which solve the resulting episodic optimization problem through convex optimization. LMI-QL relies on a convex relaxation that yields a semidefinite programming (SDP) problem with linear matrix inequalities (LMIs). LMI-QLi entails solving sequential iterations of an SDP problem. Both methods combine convex optimization with direct Q-function learning, significantly improving learning speed. A numerical case study demonstrates their advantages over existing parametrized Q-learning methods.

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arXiv2026

Smart Exploration in Reinforcement Learning using Bounded Uncertainty Models

Reinforcement learning (RL) is a powerful framework for decision-making in uncertain environments, but it often requires large amounts of data to learn an optimal policy. We address this challenge by incorporating prior model knowledge to guide exploration and accelerate the learning process. Specifically, we assume access to a model set that contains the true transition kernel and reward function. We optimize over this model set to obtain upper and lower bounds on the Q-function, which are then used to guide the exploration of the agent. We provide theoretical guarantees on the convergence of the Q-function to the optimal Q-function under the proposed class of exploring policies. Furthermore, we also introduce a data-driven regularized version of the model set optimization problem that ensures the convergence of the class of exploring policies to the optimal policy. Lastly, we show that when the model set has a specific structure, namely the bounded-parameter MDP (BMDP) framework, the regularized model set optimization problem becomes convex and simple to implement. In this setting, we also prove finite-time convergence to the optimal policy under mild assumptions. We demonstrate the effectiveness of the proposed exploration strategy, which we call BUMEX (Bounded Uncertainty Model-based Exploration), in a simulation study. The results indicate that the proposed method can significantly accelerate learning in benchmark examples. A toolbox is available at https://github.com/JvHulst/BUMEX.

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arXiv2026

Precision Specimen Positioning in Electron Microscopy through Hysteresis Compensation, Iterative Learning, and Vision-Based Sensing

Electron microscopy requires nanometer-scale specimen positioning over a long stroke. Piezo-stepper actuators are well suited for this task, but their accuracy is limited by hysteresis, mechanical misalignments, and non-collocated sensing. Prior work has addressed these limitations on simplified lab setups. However, extending to a full electron microscope stage introduces coupled nonlinear kinematics and, importantly, the absence of a dedicated point-of-interest (POI) sensor. This paper presents an integrated feedforward framework for precision positioning on such a stage inside an operational electron microscope. Per-element hysteresis compensation first linearizes the actuator response. In the absence of a dedicated POI sensor, a POI measurement is constructed from EM images through cross-correlation-based image tracking. From this measurement, we construct an encoder-based proxy for the POI position. Commutation-angle-domain iterative learning control then uses this proxy as its error signal to cancel the repeatable disturbances of stepping. Because the learned corrections are parameterized in the commutation angle, they transfer across the quasi-static range of drive frequencies. The framework reduces the POI tracking error by over 13x on the lab setup and by 7 to 12x on an operational transmission electron microscope.

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arXiv2026

Constructing VAE Latent Spaces with Prescribed Topology

Variational autoencoders (VAEs) learn low-dimensional latent representations of high-dimensional data. When the data lies on a manifold with non-Euclidean topology, the standard Gaussian prior introduces a topological mismatch that degrades reconstruction quality and prevents faithful representation. We present a constructive mathematical framework that resolves this mismatch for all manifolds that admit a product covering space. These are manifolds expressible as products of elementary factors (circles, intervals, or lines) or as quotients of such products by a finite symmetry group. The class includes cylinders, tori, Möbius strips, Klein bottles, and real projective spaces. Factorized distributions over the elementary factors yield product topologies with closed-form, decoupled KL divergences, so that each latent factor can be shaped independently while keeping training tractable. We catalogue reparametrizable encoder-prior pairs for periodic, bounded, and unbounded supports, and provide coordinate transformations that allow standard neural networks to output non-Euclidean parameters with smooth gradients. For quotient manifolds, the decoder receives group-invariant features of the covering-space coordinates, so that identified points produce identical outputs. Anchor constraints fix the coordinate system relative to the data or create soft topological holes. Experiments on synthetic manifolds and real-image datasets (rotated and cyclically shifted MNIST) confirm that a topology-matched prior aligns KL regularization with the data manifold. The resulting topology-aware models outperform the Gaussian baseline at all practically relevant regularization strengths. The code is available at https://github.com/JvHulst/VAE-Topology.

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arXiv2026

Estimating Evolving Functions with Dynamic Gaussian Processes

This paper develops the Dynamic Gaussian Process (DGP), a framework for estimating functions governed by integro-difference equations (IDEs). IDEs model continuous functions that evolve with discrete-time dynamics and arise naturally from time-discretization of linear partial differential equations (PDEs). The DGP extends Gaussian process regression to time-varying functions and extends Kalman filtering to infinite-dimensional states. The DGP posterior remains a Gaussian process with closed-form mean and covariance updates, and separable kernel structure reduces the problem to a finite-dimensional Kalman filter on basis function coefficients. This paper extends the DGP to vector-valued states, enabling the treatment of higher-order PDEs, and provides a stability and approximation error analysis for the basis function approximation. The functional L2 estimation error decomposes exactly into in-subspace and out-of-subspace contributions, and all approximation errors vanish as the number of basis functions grows. The framework is demonstrated on the heat equation and on the wave equation, the latter with a vector-valued state. Code is available at https://github.com/JvHulst/Dynamic_Gaussian_Processes.

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arXiv2026

Consistent Distributed Cooperative Localization for Ultra Large-Scale Multi-agent Systems

Cooperative localization (CL) is fundamental in emerging multi-agent systems, where agents fuse local sensing data with exchanged information to estimate their own states. At a large scale, however, tracking cross-correlations becomes infeasible, preventing the use of optimal filters. Ignoring or underestimating these correlations leads to overconfident, and thus inconsistent, estimates. Existing CL algorithms achieve good performance and consistency typically at the expense of communication, computation, or memory that scales with the network size. This is incompatible with ultra large-scale systems (ULSS) - for example, satellite mega-constellations - where per-agent resources are limited and must remain independent of the number of agents. This reveals a critical gap: no existing CL method is simultaneously well-performing, consistent, and ULSS-scalable. This paper introduces a new CL framework that addresses this gap using the recently proposed overlapping covariance intersection methodology, which enables agents to exploit limited structural information about cross-correlations without compromising consistency. The resulting CL algorithm leads to optimal conservative covariance propagation using only locally available information. The method is fully distributed, scalable to an ultra large scale, and provably recursively consistent. Simulations demonstrate substantial performance improvement over state-of-the-art consistent CL approaches while preserving scalability.

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arXiv2026

Learning myopic mixed-integer nonlinear model predictive control from expert demonstrations

Applying nonlinear model predictive control (NMPC) to systems with hybrid dynamics or discrete actions typically yields mixed-integer nonlinear programs (MINLPs), whose real-time solution remains a major challenge and limits the applicability of mixed-integer NMPC (MINMPC). This paper proposes a myopic MINMPC framework that incorporates value-function approximation to substantially reduce the online computational burden. Using Bellman's principle of optimality, we shorten the prediction horizon and append a value function learned offline from expert state-action demonstrations via inverse optimization with optimality residual minimization. A central feature is the dual treatment of discrete decisions, whereby integer constraints are relaxed during offline learning to enable KKT-residual-based value function synthesis, while the online controller enforces the true integer constraints to ensure feasibility. The learned value function induces a policy that is approximately policy-consistent with the expert demonstrations. The resulting controller achieves high closed-loop performance with a significantly shorter horizon, enabling real-time MINMPC. The effectiveness of the approach is demonstrated on the Lotka-Volterra fishing problem and a satellite attitude control system with discrete actuators.

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arXiv2026

Fuelling fusion plasmas with pellets: Can neuromorphic control outperform Sigma-Delta modulation?

Nuclear fusion is a promising clean energy source in which deuterium and tritium fuse inside a magnetically confined plasma in a tokamak, releasing energy. A key challenge on the route to practical nuclear fusion is the control of the plasma density which has to be done through adding fuel in the form of deuterium and tritium to the plasma. Pellet injection, firing frozen fuel into the plasma, is used to accomplish this. Since the injection of a pellet causes an almost instantaneous increase in particle density compared to the time scales of the plasma dynamics, the problem is of a hybrid nature in which continuous plasma dynamics are interrupted by discrete bursts of particles. In this paper, we propose a formal hybrid model for this fuelling process and we propose a new, neuron-inspired control method that treats pellets much like spikes as in a brain-like system. The neuromorphic controller offers a lightweight solution that naturally fits the hybrid character of pellet fuelling. For comparison, we also develop a hybrid model of sigma-delta modulation, which is used in current tokamaks. For both the neuromorphic controller and the sigma-delta modulation we present formal analysis results for this control problem in nuclear fusion. We derive explicit actuator and controller parameter constraints, key for controller tuning, that lead to practical stability guarantees. Numerical simulations compare the different controller variants and validate the theoretical results.

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arXiv2026

Scaled Relative Graphs and Dynamic Integral Quadratic Constraints: Connections and Computations for Nonlinear Systems

Scaled relative graphs (SRGs) enable graphical analysis and design of nonlinear systems. In this paper, we present a systematic approach for computing both soft and hard SRGs of nonlinear systems using dynamic integral quadratic constraints (IQCs). These constraints are exploited via application of the S-procedure to compute tractable SRG overbounds. In particular, we show that the multipliers associated with the IQCs define regions in the complex plane. Soft SRG computations are formulated through frequency-domain conditions, while hard SRGs are obtained via hard factorizations of multipliers and linear matrix inequalities. The overbounds are used to derive an SRG-based feedback stability result for Lur'e-type systems, providing a new graphical interpretation of classical IQC stability results with dynamic multipliers.

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arXiv2026

Analysis and Design of Reset Control Systems via Base Linear Scaled Graphs

In this letter, we prove that under mild conditions, the scaled graph of a reset control system is bounded by the scaled graph of its underlying base linear system, i.e., the system without resets. Building on this new insight, we establish that the negative feedback interconnection of a linear time-invariant plant and a reset controller is stable, if the scaled graphs of the underlying base linear components are strictly separated. This result simplifies reset system analysis, as stability conditions reduce to verifying properties of linear time-invariant systems. We exploit this result to develop a systematic approach for reset control system design. Our framework also accommodates reset systems with time-regularization, which were not addressed in the context of scaled graphs before.

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arXiv2026

Tilt-based Aberration Estimation in Transmission Electron Microscopy

Transmission electron microscopes (TEMs) enable atomic-scale imaging but suffer from aberrations caused by lens imperfections and environmental conditions, reducing image quality. These aberrations can be compensated by adjusting electromagnetic lenses, but this requires accurate estimates of the aberration coefficients, which can drift over time. This paper introduces a method for the estimation of aberrations in TEM by leveraging the relationship between an induced tilt of the electron beam and the resulting image shift. The method uses a Kalman filter (KF) to estimate the aberration coefficients from a sequence of image shifts, while accounting for the drift of the aberrations over time. The applied tilt sequence is optimized by minimizing the trace of the predicted error covariance in the KF, which corresponds to the A-optimality criterion in experimental design. We show that this optimization can be performed offline, as the cost criterion is independent of the actual measurements. The resulting non-convex optimization problem is solved using a gradient-based, receding-horizon approach with multi-starts. Additionally, we develop an approach to estimate specimen-dependent noise properties using expectation maximization (EM), which are then used to tailor the tilt pattern optimization to the specific specimen being imaged. The proposed method is validated on a real TEM set-up with several optimized tilt patterns. The results show that optimized patterns significantly outperform naive approaches and that the aberration and drift model accurately captures the underlying physical phenomena. A direct comparison with the widely used Zemlin tableau shows that the proposed method achieves comparable or higher image quality on amorphous specimens, while additionally extending to non-amorphous specimens where the Zemlin tableau cannot operate.

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arXiv2026

Bridging the Simulation-to-Reality Gap in Electron Microscope Calibration via VAE-EM Estimation

Electron microscopy has enabled many scientific breakthroughs across multiple fields. A key challenge is the tuning of microscope parameters based on images to overcome optical aberrations that deteriorate image quality. This calibration problem is challenging due to the high-dimensional and noisy nature of the diagnostic images, and the fact that optimal parameters cannot be identified from a single image. We tackle the calibration problem for Scanning Transmission Electron Microscopes (STEM) by employing variational autoencoders (VAEs), trained on simulated data, to learn low-dimensional representations of images, whereas most existing methods extract only scalar values. We then simultaneously estimate the model that maps calibration parameters to encoded representations and the optimal calibration parameters using an expectation maximization (EM) approach. This joint estimation explicitly addresses the simulation-to-reality gap inherent in data-driven methods that train on simulated data from a digital twin. We leverage the known symmetry property of the optical system to establish global identifiability of the joint estimation problem, ensuring that a unique optimum exists. We demonstrate that our approach is substantially faster and more consistent than existing methods on a real STEM, achieving a 2x reduction in estimation error while requiring fewer observations. This represents a notable advance in automated STEM calibration and demonstrates the potential of VAEs for information compression in images. Beyond microscopy, the VAE-EM framework applies to inverse problems where simulated training data introduces a reality gap and where non-injective mappings would otherwise prevent unique solutions.

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arXiv2026

Token Economy for Fair and Efficient Dynamic Resource Allocation in Congestion Games

Self-interested behavior in sharing economies often leads to inefficient aggregate outcomes compared to a centrally coordinated allocation, ultimately harming users. Yet, centralized coordination removes individual decision power. This issue can be addressed by designing rules that align individual preferences with system-level objectives. Unfortunately, rules based on conventional monetary mechanisms introduce unfairness by discriminating among users based on their wealth. To solve this problem, in this paper, we propose a token-based mechanism for congestion games that achieves efficient and fair dynamic resource allocation. Specifically, we model the token economy as a continuous-time dynamic game with finitely many boundedly rational agents, explicitly capturing their evolutionary policy-revision dynamics. We derive a mean-field approximation of the finite-population game and establish strong approximation guarantees between the mean-field and the finite-population games. This approximation enables the design of integer tolls in closed form that provably steer the aggregate dynamics toward an optimal efficient and fair allocation from any initial condition.

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arXiv2026

Safe Feedback Optimization through Control Barrier Functions

Feedback optimization refers to a class of methods that steer a control system to a steady state that solves an optimization problem. Despite tremendous progress on the topic, an important problem remains open: enforcing state constraints at all times. The difficulty in addressing it lies on mediating between the safety enforcement and the closed-loop stability, and ensuring the equivalence between closed-loop equilibria and the optimization problem's critical points. In this work, we present a feedback-optimization method that enforces state constraints at all times employing high-order control-barrier functions. We provide several results on the proposed controller dynamics, including well-posedness, safety guarantees, equivalence between equilibria and critical points, and local and global (in certain convex cases) asymptotic stability of optima. Various simulations illustrate our results.

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