arXiv subjects

Melanie N. Zeilinger

Publications and source records attributed to Melanie N. Zeilinger.

At least 37 records · Page 2Linked to original sources

arXiv2026

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↗

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

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

Model Predictive Control with Reference Learning for Soft Robotic Intracranial Pressure Waveform Modulation

This paper introduces a learning-based control framework for a soft robotic actuator system designed to modulate intracranial pressure (ICP) waveforms, which is essential for studying cerebrospinal fluid dynamics and pathological processes underlying neurological disorders. A two-layer framework is proposed to safely achieve a desired ICP waveform modulation. First, a model predictive controller (MPC) with a disturbance observer is used for offset-free tracking of the system's motor position reference trajectory under safety constraints. Second, to address the unknown nonlinear dependence of ICP on the motor position, we employ a Bayesian optimization (BO) algorithm used for online learning of a motor position reference trajectory that yields the desired ICP modulation. The framework is experimentally validated using a test bench with a brain phantom that replicates realistic ICP dynamics in vitro. Compared to a previously employed proportional-integral-derivative controller, the MPC reduces mean and maximum motor position reference tracking errors by 83 % and 73 %, respectively. In less than 20 iterations, the BO algorithm learns a motor position reference trajectory that yields an ICP waveform with the desired mean and amplitude.

cs.RO↗

arXiv2026

Safe and Near-Optimal Control with Online Dynamics Learning

Achieving both optimality and safety under unknown system dynamics is a central challenge in real-world deployment of agents. To address this, we introduce a notion of maximum safe dynamics learning, where sufficient exploration is performed within the space of safe policies. Our method executes $\textit{pessimistically}$ safe policies while $\textit{optimistically}$ exploring informative states and, despite not reaching them due to model uncertainty, ensures continuous online learning of dynamics. The framework achieves first-of-its-kind results: learning the dynamics model sufficiently $-$ up to an arbitrary small tolerance (subject to noise) $-$ in a finite time, while ensuring provably safe operation throughout with high probability and without requiring resets. Building on this, we propose an algorithm to maximize rewards while learning the dynamics $\textit{only to the extent needed}$ to achieve close-to-optimal performance. Unlike typical reinforcement learning (RL) methods, our approach operates online in a non-episodic setting and ensures safety throughout the learning process. We demonstrate the effectiveness of our approach in challenging domains such as autonomous car racing and drone navigation under aerodynamic effects $-$ scenarios where safety is critical and accurate modeling is difficult.

eess.SY↗

arXiv2026

A model predictive control framework with robust stability guarantees under unbounded disturbances

To address feasibility issues in model predictive control (MPC), most implementations relax state constraints by using slack variables and adding a penalty to the cost. We propose an alternative strategy: relaxing the initial state constraint with a penalty. Compared to state-of-the-art soft constrained MPC formulations, the proposed formulation has two key features: (i) input-to-state stability and bounds on the cumulative constraint violation for unbounded disturbances; (ii) close-to-optimal performance under nominal operating conditions. The idea is initially presented for open-loop asymptotically stable nonlinear systems by designing the penalty as a Lyapunov function, but we also show how to relax this condition to: i) Lyapunov stable systems; ii) stabilizable systems; and iii) utilizing an implicit characterization of the Lyapunov function. In the special case of linear systems, the proposed MPC formulation reduces to a quadratic program, and the offline design and online computational complexity are only marginally increased compared to a nominal design. Numerical examples demonstrate benefits compared to state-of-the-art soft-constrained MPC formulations.

math.OC↗

arXiv2026

Adaptive Economic Model Predictive Control: Performance Guarantees for Nonlinear Systems

We consider the problem of optimizing the economic performance of nonlinear constrained systems subject to uncertain time-varying parameters and bounded disturbances. In particular, we propose an adaptive economic model predictive control (MPC) framework that: (i) directly minimizes transient economic costs, (ii) addresses parametric uncertainty through online model adaptation, (iii) determines optimal setpoints online, and (iv) ensures robustness by using a tube-based approach. The proposed design ensures recursive feasibility, robust constraint satisfaction, and a transient performance bound. In case the disturbances have a finite energy and the parameter variations have a finite path length, the asymptotic average performance is (approximately) not worse than the performance obtained when operating at the best reachable steady-state. We highlight performance benefits in a numerical example involving a chemical reactor with unknown time-invariant and time-varying parameters.

eess.SY↗

arXiv2026

Optimal kernel regression bounds under energy-bounded noise

Non-conservative uncertainty bounds are key for both assessing an estimation algorithm's accuracy and in view of downstream tasks, such as its deployment in safety-critical contexts. In this paper, we derive a tight, non-asymptotic uncertainty bound for kernel-based estimation, which can also handle correlated noise sequences. Its computation relies on a mild norm-boundedness assumption on the unknown function and the noise, returning the worst-case function realization within the hypothesis class at an arbitrary query input location. The value of this function is shown to be given in terms of the posterior mean and covariance of a Gaussian process for an optimal choice of the measurement noise covariance. By rigorously analyzing the proposed approach and comparing it with other results in the literature, we show its effectiveness in returning tight and easy-to-compute bounds for kernel-based estimates.

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.

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arXiv2025

L4acados: Learning-based models for acados, applied to Gaussian process-based predictive control

Incorporating learning-based models, such as artificial neural networks or Gaussian processes, into model predictive control (MPC) strategies can significantly improve control performance and online adaptation capabilities for real-world applications. Still, enabling state-of-the-art implementations of learning-based models for MPC is complicated by the challenge of interfacing machine learning frameworks with real-time optimal control software. This work aims at filling this gap by incorporating external sensitivities in sequential quadratic programming solvers for nonlinear optimal control. To this end, we provide L4acados, a general framework for incorporating Python-based dynamics models in the real-time optimal control software acados. By computing external sensitivities via a user-defined Python module, L4acados enables the implementation of MPC controllers with learning-based residual models in acados, while supporting parallelization of sensitivity computations when preparing the quadratic subproblems. We demonstrate significant speed-ups and superior scaling properties of L4acados compared to available software using a neural-network-based control example. Last, we provide an efficient and modular real-time implementation of Gaussian process-based MPC using L4acados, which is applied to two hardware examples: autonomous miniature racing, as well as motion control of a full-scale autonomous vehicle for an ISO lane change maneuver.

eess.SY↗

arXiv2025

MHE under parametric uncertainty -- Robust state estimation without informative data

In this paper, we study joint state and parameter estimation for general nonlinear systems with uncertain parameters and persistent process and measurement noise. In particular, we are interested in stability properties of the resulting state estimate in the absence of persistency of excitation (PE). With a simple academic example, we show that existing moving horizon estimation (MHE) approaches for joint state and parameter estimation as well as classical adaptive observers can result in diverging state estimates in the absence of PE, even if the noise is small. We propose an MHE formulation involving a regularization based on a constant prior estimate of the unknown system parameters. Only assuming the existence of a stable state estimator, we prove that the proposed MHE approach results in practically robustly stable state estimates irrespective of PE. We discuss the relation of the proposed MHE formulation to state-of-the-art results from MHE and adaptive estimation. The properties of the proposed MHE approach are illustrated with a numerical example of a car with unknown tire friction parameters.

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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.

eess.SY↗

arXiv2025

Approximate non-linear model predictive control with safety-augmented neural networks

Model predictive control (MPC) achieves stability and constraint satisfaction for general nonlinear systems, but requires computationally expensive online optimization. This paper studies approximations of such MPC controllers via neural networks (NNs) to achieve fast online evaluation. We propose safety augmentation that yields deterministic guarantees for convergence and constraint satisfaction despite approximation inaccuracies. We approximate the entire input sequence of the MPC with NNs, which allows us to verify online if it is a feasible solution to the MPC problem. We replace the NN solution by a safe candidate based on standard MPC techniques whenever it is infeasible or has worse cost. Our method requires a single evaluation of the NN and forward integration of the input sequence online, which is fast to compute on resource-constrained systems. The proposed control framework is illustrated using two numerical non-linear MPC benchmarks of different complexity, demonstrating computational speedups that are orders of magnitude higher than online optimization. In the examples, we achieve deterministic safety through the safety-augmented NNs, where a naive NN implementation fails.

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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.

math.OC↗

arXiv2025

Approximate predictive control barrier function for discrete-time systems

We propose integrating an approximation of a predictive control barrier function (PCBF) in a safety filter framework, resulting in a prediction horizon independent formulation. The PCBF is defined through the value function of an optimal control problem and ensures invariance as well as stability of a safe set within a larger domain of attraction. We provide a theoretical analysis of the proposed algorithm, establishing input-to-state stability of the safe set with respect to approximation errors as well as exogenous disturbances. Furthermore, we propose a continuous extension of the PCBF within the safe set, reducing the impact of learning errors on filter interventions. We demonstrate the stability properties and computational advantages of the proposed algorithm on a linear system example and its application as a safety filter for miniature race cars in simulation.

eess.SY↗

arXiv2025

Robust Nonlinear Optimal Control via System Level Synthesis

This paper addresses the problem of finite horizon constrained robust optimal control for nonlinear systems subject to norm-bounded disturbances. To this end, the underlying uncertain nonlinear system is decomposed based on a first-order Taylor series expansion into a nominal system and an error (deviation) described as an uncertain linear time-varying system. This decomposition allows us to leverage system level synthesis to jointly optimize an affine error feedback, a nominal nonlinear trajectory, and, most importantly, a dynamic linearization error over-bound used to ensure robust constraint satisfaction for the nonlinear system. The proposed approach thereby results in less conservative planning compared with state-of-the-art techniques. We demonstrate the benefits of the proposed approach to control the rotational motion of a rigid body subject to state and input constraints.

math.OC↗