W. P. M. H. Heemels

Leonardo Pedroso, W. P. M. H. Heemels, Pedro Batista

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.

M. C. F. Donkers, P. Tabuada, W. P. M. H. Heemels

In this paper, we present two control laws that are tailored for control applications in which computational and/or communication resources are scarce. Namely, we consider minimum attention control, where the `attention' that a control task requires is minimised given certain performance requirements, and anytime attention control, where the performance under the `attention' given by a scheduler is maximised. Here, we interpret `attention' as the inverse of the time elapsed between two consecutive executions of a control task. By focussing on linear plants, by allowing for only a finite number of possible intervals between two subsequent executions of the control task, by making a novel extension to the notion of control Lyapunov functions and taking these novel extended control Lyapunov function to be infinity-norm-based, we can formulate the aforementioned control problems as online linear programs, which can be solved efficiently. Furthermore, we provide techniques to construct suitable infinity-norm-based extended control Lyapunov functions for our purposes. Finally, we illustrate the resulting control laws using numerical examples. In particular, we show that minimum attention control outperforms an alternative implementation-aware control law available in the literature.

Jilles S. van Hulst, Erik M. Franken, Bart J. Janssen et al.

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.

Leonardo Pedroso, W. P. M. H. Heemels, Pedro Batista

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 introduces a generalized CI framework, called overlapping covariance intersection (OCI), which 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.

Leonardo Pedroso, Andrea Agazzi, W. P. M. H. Heemels et al.

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.

Leonardo Pedroso, Pedro Batista, W. P. M. H. Heemels

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.

J. S. van Hulst, W. P. M. H. Heemels, D. J. Antunes

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.

Timo de Groot, Tom Oomen, W. P. M. H. Heemels et al.

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.

T. de Groot, W. P. M. H. Heemels, S. J. A. M. van den Eijnden

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.

Christopher Anthony Orrico, W. P. M. H. Heemels, Dinesh Krishnamoorthy

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.

L. L. T. C. Jansen, E. Petri, M. van Berkel et al.

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.