arXiv subjects

Melanie N. Zeilinger

Publications and source records attributed to Melanie N. Zeilinger.

At least 19 recordsLinked to original sources

arXiv2026

Scalable Gaussian Process Regression via Deterministic Trigonometric Features: Uniform Bounds for Safe Model Predictive Control

Learning-based Model Predictive Control (MPC) using Gaussian processes (GPs) is an effective approach for safe control in the presence of model mismatch. High-probability safety guarantees typically require uncertainty bounds that hold uniformly over the entire state--input domain, but existing bounds are available only for full GP regression. Since exact GP inference scales poorly with the number of data points, its deployment is impractical in large-data regimes. We close this gap by developing a scalable GP framework that admits the derivation of uniform uncertainty bounds. We formalize a deterministic trigonometric feature Gaussian process (DTF-GP), a finite-dimensional kernel approximation based on discretized trigonometric features that reduces GP regression to Bayesian linear regression in feature space. We derive a high-probability uniform uncertainty bound for the proposed DTF-GP and provide its closed-form solution for the squared-exponential kernel case. Finally, we integrate the DTF-GP into a learning-based MPC scheme and demonstrate that it provides high-probability safety guarantees and exploration performance comparable to a full GP while improving computational efficiency in large-data regimes.

eess.SY↗

arXiv2026

Anytime Plug-and-Play Control with Contract-Based Distributed MPC

A central challenge in many mobile multi-robot applications is that communication topologies are inherently time-varying. Agents may enter or exit the network and such changes cannot generally be restricted a priori. This work introduces a distributed multi-agent control algorithm based on local communication that supports anytime agent joining and leaving the communication network without centralized coordination. The method scales efficiently with the number of agents by relying on a distance-based neighbor definition and on contracts derived from predicted trajectories. The resulting contract constraints guarantee collision avoidance and constraint satisfaction. We validate the proposed method in an autonomous multi-agent driving scenario, demonstrating effective collision avoidance in high-speed, dynamic environments with agents moving in opposite directions, in both simulated and real-world experiments.

math.OC↗

arXiv2026

VISION-SLS: Safe Perception-Based Control from Learned Visual Representations via System Level Synthesis

We propose VISION-SLS, a method for nonlinear output-feedback control from high-resolution RGB images which provides robust constraint satisfaction guarantees under calibrated uncertainty bounds despite partial observability, sensor noise, and nonlinear dynamics. To enable scalability while retaining guarantees, we propose: (i) a learned low-dimensional observation map from pretrained visual features with state-dependent error bounds, and (ii) a causal affine time-varying output-feedback policy optimized via System Level Synthesis (SLS). We develop a scalable, novel solver for the resulting nonconvex program that leverages sequential convex programming coupled with efficient Riccati recursions. On two simulated visuomotor tasks (a 4D car and a 10D quadrotor) with >= 512 x 512 pixels and a 59D humanoid task with partial observability, our method enables safe, information-gathering behavior that reduces uncertainty while guaranteeing constraint satisfaction with empirically-calibrated error bounds. We also validate our method on hardware, safely controlling a ground vehicle from onboard images, outperforming baselines in safety rate and solve times. Together, these results show that learned visual abstractions coupled with an efficient solver make SLS-based safe visuomotor output-feedback practical at scale. The code implementation of our method is available at https://github.com/trustworthyrobotics/VISION-SLS.

cs.RO↗

arXiv2026

Efficient Uniform Feasible-Set Sampling for Approximate Linear MPC

Model Predictive Control (MPC) offers safe and near-optimal control but suffers from high computational costs. Approximate MPC (AMPC) mitigates this by learning a cheaper surrogate policy, typically by training a neural network on state-MPC input pairs. Generating training data is a major bottleneck, requiring solving the MPC for numerous states sampled from its feasible set. Since this feasible set is implicitly defined and unknown, efficient sampling is nontrivial but crucial. We propose the linear MPC Hit-and-Run (LMPC-HR) sampler for linear MPC with polyhedral constraints. We identify the feasible set boundaries along search directions, a crucial step within HR, by formulating the problem as a convex linear program, replacing expensive iterative searches with a single optimization step. A numerical study demonstrates that LMPC-HR reduces the computational cost of generating uniformly distributed samples from the feasible set by an order of magnitude compared to standard baselines.

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arXiv2026

Bridging RL and MPC for mixed-integer optimal control with application to Formula 1 race strategies

We propose a hybrid reinforcement learning (RL) and model predictive control (MPC) framework for mixed-integer optimal control, where discrete variables enter the cost and dynamics but not the constraints. Existing hierarchical approaches use RL only for the discrete action space, leaving continuous optimization to MPC. Unlike these methods, we train the RL agent on the full hybrid action space, ensuring consistency with the cost of the underlying Markov decision process. During deployment, the RL actor is rolled out over the prediction horizon to parametrize an integer-free nonlinear MPC through the discrete action sequence and provide a continuous warm-start. The learned critic serves as a terminal cost to capture long-term performance. We prove recursive feasibility, and validate the framework on a Formula 1 race strategy problem. The hybrid method achieves near-optimal performance relative to an offline mixed-integer nonlinear program benchmark, outperforming a standalone RL agent. Moreover, the hybrid scheme enables adaptation to unseen disturbances through modular MPC extensions at zero retraining cost.

eess.SY↗

arXiv2026

Distributed Predictive Control Barrier Functions: Towards Scalable Safety Certification in Modular Multi-Agent Systems

We consider safety-critical multi-agent systems with distributed control architectures and potentially varying network topologies. While learning-based distributed control enables scalability and high performance, a lack of formal safety guarantees in the face of unforeseen disturbances and unsafe network topology changes may lead to system failure. To address this challenge, we introduce structured control barrier functions (s-CBFs) as a multi-agent safety framework. The s-CBFs are augmented to a distributed predictive control barrier function (D-PCBF), a predictive, optimization-based safety layer that uses model predictions to guarantee recoverable safety at all times. The proposed approach enables a permissive yet formal plug-and-play protocol, allowing agents to join or leave the network while ensuring safety recovery if a change in network topology requires temporarily unsafe behavior. We validate the formulation through simulations and real-time experiments of a miniature race-car platoon.

eess.SY↗

arXiv2026

Optimistic Online LQR via Intrinsic Rewards

Optimism in the face of uncertainty is a popular approach to balance exploration and exploitation in reinforcement learning. Here, we consider the online linear quadratic regulator (LQR) problem, i.e., to learn the LQR corresponding to an unknown linear dynamical system by adapting the control policy online based on closed-loop data collected during operation. In this work, we propose Intrinsic Rewards LQR (IR-LQR), an optimistic online LQR algorithm that applies the idea of intrinsic rewards originating from reinforcement learning and the concept of variance regularization to promote uncertainty-driven exploration. IR-LQR typically retains the structure of a standard LQR synthesis problem by only modifying the cost function, resulting in an intuitively pleasing, simple, computationally cheap, and efficient algorithm. This is in contrast to existing optimistic online LQR formulations that rely on more complicated iterative search algorithms or solve computationally demanding optimization problems. We show that IR-LQR achieves the optimal worst-case regret rate of $\sqrt{T}$, and compare it to various state-of-the-art online LQR algorithms via numerical experiments carried out on an aircraft pitch angle control and an unmanned aerial vehicle example.

eess.SY↗

arXiv2026

Real-Time Online Learning for Model Predictive Control using a Spatio-Temporal Gaussian Process Approximation

Learning-based model predictive control (MPC) can enhance control performance by correcting for model inaccuracies, enabling more precise state trajectory predictions than traditional MPC. A common approach is to model unknown residual dynamics as a Gaussian process (GP), which leverages data and also provides an estimate of the associated uncertainty. However, the high computational cost of online learning poses a major challenge for real-time GP-MPC applications. This work presents an efficient implementation of an approximate spatio-temporal GP model, offering online learning at constant computational complexity. It is optimized for GP-MPC, where it enables improved control performance by learning more accurate system dynamics online in real-time, even for time-varying systems. The performance of the proposed method is demonstrated by simulations and hardware experiments in the exemplary application of autonomous miniature racing.

eess.SY↗

arXiv2026

Optimal uncertainty bounds for multivariate kernel regression under bounded noise: A Gaussian process-based dual function

Non-conservative uncertainty bounds are essential for making reliable predictions about latent functions from noisy data, and thus, a key enabler for safe learning-based control. In this domain, kernel methods such as Gaussian process regression are established techniques, thanks to their inherent uncertainty quantification mechanism. Still, existing bounds either pose strong assumptions on the underlying noise distribution, are conservative, do not directly apply in the multi-output case, or are difficult to integrate into downstream tasks. This paper addresses these limitations by presenting a tight, deterministic bound for multi-output functions in Reproducing Kernel Hilbert Spaces (RKHSs) subject to bounded noise. It is obtained through an unconstrained, duality-based formulation, which shares the same structure as classic Gaussian process confidence bounds, and can thus be straightforwardly integrated into downstream optimization pipelines. We show that the proposed bound generalizes existing results and illustrate its application using an example inspired by quadrotor dynamics learning.

cs.LG↗

arXiv2025

Learning-based Approximate Model Predictive Control for an Impact Wrench Tool

Learning-based model predictive control has emerged as a powerful approach for handling complex dynamics in mechatronic systems, enabling data-driven performance improvements while respecting safety constraints. However, when computational resources are severely limited, as in battery-powered tools with embedded processors, existing approaches struggle to meet real-time requirements. In this paper, we address the problem of real-time torque control for impact wrenches, where high-frequency control updates are necessary to accurately track the fast transients occurring during periodic impact events, while maintaining high-performance safety-critical control that mitigates harmful vibrations and component wear. The key novelty of the approach is that we combine data-driven model augmentation through Gaussian process regression with neural network approximation of the resulting control policy. This insight allows us to deploy predictive control on resource-constrained embedded platforms while maintaining both constraint satisfaction and microsecond-level inference times. The proposed framework is evaluated through numerical simulations and hardware experiments on a custom impact wrench testbed. The results show that our approach successfully achieves real-time control suitable for high-frequency operation while maintaining constraint satisfaction and improving tracking accuracy compared to baseline PID control.

eess.SY↗

arXiv2025

Unifying Sequential Quadratic Programming and Linear-Parameter-Varying Algorithms for Real-Time Model Predictive Control

This paper presents a unified framework that connects sequential quadratic programming (SQP) and the iterative linear-parameter-varying model predictive control (LPV-MPC) technique. Using the differential formulation of the LPV-MPC, we demonstrate how SQP and LPV-MPC can be unified through a specific choice of scheduling variable and the 2nd Fundamental Theorem of Calculus (FTC) embedding technique and compare their convergence properties. This enables the unification of the zero-order approach of SQP with the LPV-MPC scheduling technique to enhance the computational efficiency of robust and stochastic MPC problems. To demonstrate our findings, we compare the two schemes in a simulation example. Finally, we present real-time feasibility and performance of the zero-order LPV-MPC approach by applying it to Gaussian process (GP)-based MPC for autonomous racing with real-world experiments.

eess.SY↗

arXiv2025

Statistically Consistent Approximate Model Predictive Control

Model Predictive Control (MPC) offers rigorous safety and performance guarantees but is computationally intensive. Approximate MPC (AMPC) aims to circumvent this drawback by learning a computationally cheaper surrogate policy. Common approaches focus on imitation learning (IL) via behavioral cloning (BC), minimizing a mean-squared-error loss on a collection of state-input pairs. However, BC fundamentally fails to provide accurate approximations when MPC solutions are set-valued due to non-convex constraints or local minima. We propose a two-stage IL procedure to accurately approximate nonlinear, potentially set-valued MPC policies. The method integrates an approximation of the MPC's optimal value function into a one-step look-ahead loss function, and thereby embeds the MPC's constraint and performance objectives into the IL objective. This is achieved by adopting a stabilizing soft constrained MPC formulation, which reflects constraint violations in the optimal value function by combining a constraint tightening with slack penalties. We prove statistical consistency for policies that exactly minimize our IL objective, implying convergence to a safe and stabilizing control law, and establish input-to-state stability guarantees for approximate minimizers. Simulations demonstrate improved performance compared to BC.

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arXiv2025

Stability of Certainty-Equivalent Adaptive LQR for Linear Systems with Unknown Time-Varying Parameters

Standard model-based control design deteriorates when the system dynamics change during operation. To overcome this challenge, online and adaptive methods have been proposed in the literature. In this work, we consider the class of discrete-time linear systems with unknown time-varying parameters. We propose a simple, modular, and computationally tractable approach by combining two classical and well-known building blocks from estimation and control: the least mean square filter and the certainty-equivalent linear quadratic regulator. Despite both building blocks being simple and off-the-shelf, our analysis shows that they can be seamlessly combined to a powerful pipeline with stability guarantees. Namely, finite-gain $\ell^2$-stability of the closed-loop interconnection of the unknown system, the parameter estimator, and the controller is proven, despite the presence of unknown disturbances and time-varying parametric uncertainties. Real-world applicability of the proposed algorithm is showcased by simulations carried out on a nonlinear planar quadrotor.

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arXiv2025

Eigenvalues as a Metric for Memory Dynamics in Sequence Models

While softmax attention drives state-of-the-art performance in sequence modeling, its quadratic complexity motivates linear alternatives such as state space models (SSMs). Structural differences between the two model classes, however, hinder direct comparisons of their memory dynamics, creating the need for a common metric to analyze, interpret, and improve their information processing capabilities. Inspired by recent advances in SSM performance driven by eigenvalue-guided insights, we leverage the dynamical systems framework to bring attention models into a unified analytical framework with SSMs. This allows us to perform a structured analysis, which investigates the applicability of an eigenvalue-spectrum memory dynamics metric to attention models. To this end, we first conduct an extensive empirical study across diverse attention-based models and SSMs on a range of benchmarks. We show that, for both model classes, eigenvalues influence key aspects of memory and long-range dependency modeling, revealing spectral signatures that align with task requirements. Building on these findings, we show how spectral signatures can motivate architectural modifications, how they can be guided through the training process, and how they can provide information about feature importance. The results thereby enable and emphasize the role of eigenvalue analysis as a principled metric for interpreting, explaining, and ultimately improving the capabilities of sequence models.

cs.LG↗

arXiv2025

Design Principles for Sequence Models via Coefficient Dynamics

Deep sequence models, ranging from Transformers and State Space Models (SSMs) to more recent approaches such as gated linear RNNs, fundamentally compute outputs as linear combinations of past value vectors. To draw insights and systematically compare such architectures, we develop a unified framework that makes this output operation explicit, by casting the linear combination coefficients as the outputs of autonomous linear dynamical systems driven by impulse inputs. This viewpoint, in spirit substantially different from approaches focusing on connecting linear RNNs with linear attention, reveals a common mathematical theme across diverse architectures and crucially captures softmax attention, on top of RNNs, SSMs, and related models. In contrast to new model proposals that are commonly evaluated on benchmarks, we derive design principles linking architectural choices to model properties. Thereby identifying tradeoffs between expressivity and efficient implementation, geometric constraints on input selectivity, and stability conditions for numerically stable training and information retention. By connecting several insights and observations from recent literature, the framework both explains empirical successes of recent designs and provides guiding principles for systematically designing new sequence model architectures.

cs.LG↗

arXiv2025

Physics-informed learning under mixing: How physical knowledge speeds up learning

A major challenge in physics-informed machine learning is to understand how the incorporation of prior domain knowledge affects learning rates when data are dependent. Focusing on empirical risk minimization with physics-informed regularization, we derive complexity-dependent bounds on the excess risk in probability and in expectation. We prove that, when the physical prior information is aligned, the learning rate improves from the (slow) Sobolev minimax rate to the (fast) optimal i.i.d. one without any sample-size deflation due to data dependence.

cs.LG↗

arXiv2025

A quantitative analysis of intraventricular bioimpedance in an in vivo pilot study with contextual pressure measurements

Hydrocephalus is a neurological condition characterized by disturbed cerebrospinal fluid (CSF) dynamics and is typically treated with shunt systems that drain excessive CSF out of the ventricular system. Continuous monitoring of ventricular CSF volume, however, remains a major unmet need in the clinical management of this condition. While intraventricular bioimpedance (BI) has been proposed as a potential marker of CSF volume, prior investigations have been limited to simulations, in vitro phantoms, and small animal models. This work presents the development of a measurement system for intraventricular BI and its evaluation in a large animal model. The measurement system was first validated in vitro using a mechatronic test bench replicating physiological CSF dynamics and subsequently applied in an in vivo pilot study with concurrent CSF and blood pressure monitoring. Time series analysis of the recorded signals revealed physiological BI waveform components linked to the cardiac and respiratory cycles. In addition, changes in BI following CSF volume alterations induced through intrathecal bolus infusions of artificial CSF were observed and found to be correlated to changes in CSF and blood pressures. These results provide the first in vivo evidence in a large animal model that BI reflects CSF dynamics as well as cerebral hemodynamics. Complementing intracranial pressure and CSF drainage measurements in smart shunt systems with BI could enable more comprehensive patient monitoring and physiologically informed control of hydrocephalus therapy.

physics.med-ph↗

arXiv2025

Guaranteed Robust Nonlinear MPC via Disturbance Feedback

Robots must satisfy safety-critical state and input constraints despite disturbances and model mismatch. We introduce a robust model predictive control (RMPC) formulation that is fast, scalable, and compatible with real-time implementation. Our formulation guarantees robust constraint satisfaction, input-to-state stability (ISS) and recursive feasibility. The key idea is to decompose the uncertain nonlinear system into (i) a nominal nonlinear dynamic model, (ii) disturbance-feedback controllers, and (iii) bounds on the model error. These components are optimized jointly using sequential convex programming. The resulting convex subproblems are solved efficiently using a recent disturbance-feedback MPC solver. The approach is validated across multiple dynamics, including a rocket-landing problem with steerable thrust. An open-source implementation is available at https://github.com/antoineleeman/robust-nonlinear-mpc.

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