arXiv subjects

Rolf Findeisen

Publications and source records attributed to Rolf Findeisen.

At least 19 recordsLinked to original sources

arXiv2026

Uncertainty-Aware Fusion for Resilient Distributed Radar Sensing

Distributed radar sensing enables safe and resilient operation in mobile robotic and vehicular systems by combining multiple local views of the scene. In this paper, we consider a moving agent equipped with a frequency modulated continuous wave (FMCW) radar that fuses its local measurements with those of surrounding static radar sensors to reduce the uncertainty in target state estimation. The benefit of sharing measurements over capacity-limited wireless links come at the expense of two competing degradation mechanisms: quantization distortion, which increases the effective noise floor, and latency, which causes the received information to age. A unified framework is thus needed to quantify how individual radars contribute to uncertainty reduction under limited communication resources. To this end, we derive the Cramer-Rao lower bound (CRLB) for the fused target state by combining local Fisher information matrices (FIMs) through coordinate transformations, incorporating distortion bounds from rate-distortion theory and information aging via a state transition model. We show that the resulting expression reveals a fundamental tradeoff between update rate and quantization fidelity governed by the available channel capacity. Our numerical simulations illustrate this tradeoff and demonstrate that a careful choice of system parameters (e.g., selected radar systems, quantization, update rate) is necessary for maximum uncertainty reduction.

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arXiv2026

Model Predictive Control for Constrained Linear Positive Systems on Graphs

Positive systems describing networks with inherently non-negative states and inputs arise naturally in routing, logistics, and compartmental modelling. We consider problems modelled as positive linear systems in incidence form with linear cost. The addition of capacity constraints on states (storage) and inputs (flows between nodes) significantly increases the problem complexity. Leveraging the analytic structure of the unconstrained problem, an explicit suboptimal admissible controller is constructed. This yields graph-computable performance bounds and a minimum stabilising horizon length for a model predictive controller without terminal conditions. A convex program enables efficient computation of the optimal bound and horizon. These results highlight how system structure enables explicit MPC guarantees that are typically not available.

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arXiv2026

Real-time Gaussian Process based Approximate Model Predictive Trajectory Tracking Control for Autonomous Vehicles

Applying model predictive control on embedded systems remains challenging due to the high computational cost of solving optimal control problems. To address this limitation, computationally efficient Gaussian process approximations of the implicit model predictive control law can be employed. However, for trajectory-tracking applications, the large amount of training data required for successful generalization across distinct reference trajectories poses a significant challenge. To improve data efficiency, we propose to transform the model into curvilinear coordinates around the reference trajectory. Secondly, we use a nominal feedforward component, allowing the Gaussian process to learn only the residual control input, making the approximation of a trajectory-tracking controller feasible. To underline the applicability of the approach, we deploy the controller on a Raspberry Pi in a small-scale vehicle and validate it experimentally. Compared to a model predictive control implementation using real-time iterations, the Gaussian process based approximation computes control inputs about five times faster while achieving similar closed-loop tracking performance.

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arXiv2026

Data-Driven Reachability Analysis with Optimal Input Design

This paper addresses the conservatism in data-driven reachability analysis for discrete-time linear systems subject to bounded process noise, where the system matrices are unknown and only input--state trajectory data are available. Building on the constrained matrix zonotope (CMZ) framework, two complementary strategies are proposed to reduce conservatism in reachable-set over-approximations. First, the standard Moore--Penrose pseudoinverse is replaced with a row-norm-minimizing right inverse computed via a second-order cone program (SOCP), which directly reduces the size of the resulting model set, yielding tighter generators and less conservative reachable sets. Second, an online A-optimal input design strategy is introduced to improve the informativeness of the collected data and the conditioning of the resulting model set, thereby reducing uncertainty. The proposed framework extends naturally to piecewise affine systems through mode-dependent data partitioning. Numerical results on a five-dimensional stable LTI system and a two-dimensional piecewise affine system demonstrate that combining designed inputs with the row-norm right inverse significantly reduces conservatism compared to a baseline using random inputs and the pseudoinverse, leading to tighter reachable sets for safety verification.

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arXiv2026

Bridging Data-Driven Reachability Analysis and Statistical Estimation via Constrained Matrix Convex Generators

Data-driven reachability analysis enables safety verification when first-principles models are unavailable. This requires constructing sets of system models consistent with measured trajectories and noise assumptions. Existing approaches rely on zonotopic or box-based approximations, which do not fit the geometry of common noise distributions such as Gaussian disturbances and can lead to significant conservatism, especially in high-dimensional settings. This paper builds on ellipsotope-based representations to introduce mixed-norm uncertainty sets for data-driven reachability. The highest-density region defines the exact minimum-volume noise confidence set, while Constrained Convex Generators (CCG) and their matrix counterpart (CMCG) provide compatible geometric representations at the noise and parameter level. We show that the resulting CMCG coincides with the maximum-likelihood confidence ellipsoid for Gaussian disturbances, while remaining strictly tighter than constrained matrix zonotopes for mixed bounded-Gaussian noise. For non-convex noise distributions such as Gaussian mixtures, a minimum-volume enclosing ellipsoid provides a tractable convex surrogate. We further prove containment of the CMCG times CCG product and bound the conservatism of the Gaussian-Gaussian interaction. Numerical examples demonstrate substantially tighter reachable sets compared to box-based approximations of Gaussian disturbances. These results enable less conservative safety verification and improve the accuracy of uncertainty-aware control design.

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arXiv2026

Efficient Controller Learning from Human Preferences and Numerical Data Via Multi-Modal Surrogate Models

Tuning control policies manually to meet high-level objectives is often time-consuming. Bayesian optimization provides a data-efficient framework for automating this process using numerical evaluations of an objective function. However, many systems, particularly those involving humans, require optimization based on subjective criteria. Preferential Bayesian optimization addresses this by learning from pairwise comparisons instead of quantitative measurements, but relying solely on preference data can be inefficient. We propose a multi-fidelity, multi-modal Bayesian optimization framework that integrates low-fidelity numerical data with high-fidelity human preferences. Our approach employs Gaussian process surrogate models with both hierarchical, autoregressive and non-hierarchical, coregionalization-based structures, enabling efficient learning from mixed-modality data. We illustrate the framework by tuning an autonomous vehicle's trajectory planner, showing that combining numerical and preference data significantly reduces the need for experiments involving the human decision maker while effectively adapting driving style to individual preferences.

cs.LG↗

arXiv2026

On Data-Driven Unbiased Predictors using the Koopman Operator

The Koopman operator and its data-driven approximations, such as extended dynamic mode decomposition (EDMD), are widely used for analysing, modelling, and controlling nonlinear dynamical systems. However, when the true Koopman eigenfunctions cannot be identified from finite data, multi-step predictions may suffer from structural inaccuracies and systematic bias. To address this issue, we analyse the first and second moments of the multi-step prediction residual. By decomposing the residual into contributions from the one-step approximation error and the propagation of accumulated inaccuracies, we derive a closed-form expression characterising these effects. This analysis enables the development of a novel and computationally efficient algorithm that enforces unbiasedness and reduces variance in the resulting predictor. The proposed method is validated in numerical simulations, showing improved uncertainty properties compared to standard EDMD. These results lay the foundation for uncertainty-aware and unbiased Koopman-based prediction frameworks that can be extended to controlled and stochastic systems.

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arXiv2025

High-Dimensional Surrogate Modeling for Closed-Loop Learning of Neural-Network-Parameterized Model Predictive Control

Learning controller parameters from closed-loop data has been shown to improve closed-loop performance. Bayesian optimization, a widely used black-box and sample-efficient learning method, constructs a probabilistic surrogate of the closed-loop performance from few experiments and uses it to select informative controller parameters. However, it typically struggles with dense high-dimensional controller parameterizations, as they may appear, for example, in tuning model predictive controllers, because standard surrogate models fail to capture the structure of such spaces. This work suggests that the use of Bayesian neural networks as surrogate models may help to mitigate this limitation. Through a comparison between Gaussian processes with Matern kernels, finite-width Bayesian neural networks, and infinite-width Bayesian neural networks on a cart-pole task, we find that Bayesian neural network surrogate models achieve faster and more reliable convergence of the closed-loop cost and enable successful optimization of parameterizations with hundreds of dimensions. Infinite-width Bayesian neural networks also maintain performance in settings with more than one thousand parameters, whereas Matern-kernel Gaussian processes rapidly lose effectiveness. These results indicate that Bayesian neural network surrogate models may be suitable for learning dense high-dimensional controller parameterizations and offer practical guidance for selecting surrogate models in learning-based controller design.

cs.LG↗

arXiv2025

Real-Time Non-Smooth MPC for Switching Systems: Application to a Three-Tank Process

Real-time model predictive control of non-smooth switching systems remains challenging due to discontinuities and the presence of discrete modes, which complicate numerical integration and optimization. This paper presents a real-time feasible non-smooth model predictive control scheme for a physical three-tank process, implemented without mixed-integer formulations. The approach combines Filippov system modeling with finite elements and switch detection for time discretization, leading to a finite-dimensional optimal control problem formulated as a mathematical program with complementarity constraints. The mathematical program is solved via a homotopy of smooth nonlinear programs. We introduce modeling adjustments that make the three-tank dynamics numerically tractable, including additional modes to avoid non-Lipschitz points and undefined function values. Hardware experiments demonstrate efficient handling of switching events, mode-consistent tracking across reference changes, correct boundary handling, and constraint satisfaction. Furthermore, we investigate the impact of model mismatch and show that the tracking performance and computation times remain within real-time limits for the chosen sampling time. The complete controller is implemented using the non-smooth optimal control framework NOSNOC

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arXiv2025

Time-Series-Informed Closed-loop Learning for Sequential Decision Making and Control

Closed-loop performance of sequential decision making algorithms, such as model predictive control, depends strongly on the choice of controller parameters. Bayesian optimization allows learning of parameters from closed-loop experiments, but standard Bayesian optimization treats this as a black-box problem and ignores the temporal structure of closed-loop trajectories, leading to slow convergence and inefficient use of experimental resources. We propose a time-series-informed multi-fidelity Bayesian optimization framework that aligns the fidelity dimension with closed-loop time, enabling intermediate performance evaluations within a closed-loop experiment to be incorporated as lower-fidelity observations. Additionally, we derive probabilistic early stopping criteria to terminate unpromising closed-loop experiments based on the surrogate model's posterior belief, avoiding full episodes for poor parameterizations and thereby reducing resource usage. Simulation results on a nonlinear control benchmark demonstrate that, compared to standard black-box Bayesian optimization approaches, the proposed method achieves comparable closed-loop performance with roughly half the experimental resources, and yields better final performance when using the same resource budget, highlighting the value of exploiting temporal structure for sample-efficient closed-loop controller tuning.

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arXiv2025

Shaping the Koopman dictionary by learning on the Grassmannian

Extended dynamic mode decomposition (EDMD) is a powerful tool to construct linear predictors of nonlinear dynamical systems by approximating the action of the Koopman operator on a subspace spanned by finitely many observable functions. However, its accuracy heavily depends on the choice of the observables, which remains a challenge. We propose a systematic framework to identify and shape observable dictionaries, reduce projection errors, and achieve approximately invariant subspaces. To this end, we leverage optimisation on the Grassmann manifold and exploit inherent geometric properties for computational efficiency. Numerical results demonstrate improved prediction accuracy and efficiency. In conclusion, we propose a novel approach to efficiently shape the Koopman dictionary using differential-geometric concepts for optimisation on manifolds resulting in enhanced data-driven Koopman surrogates for nonlinear dynamical systems.

math.DS↗

arXiv2025

Bang-Ride Optimal Control: Monotonicity, External Positivity, and Fast Battery Charging

This work studies a class of optimal control problems with scalar inputs and general constraints, whose solutions follow a bang-ride pattern that always activates a constraint and enables efficient numerical computation. As a motivating example, fast battery charging leads to computationally demanding optimal control problems when detailed electrochemical models are used. Recently proposed optimization-free heuristics reduce this computational cost while producing input profiles observed in practice, following a bang-ride pattern and applying the maximum feasible input. We investigate when such heuristics satisfy necessary optimality conditions. By leveraging Pontryagin's maximum principle, we unify and formalize existing insights on the bang-ride structure and on the optimal control attaining the maximum feasible input under monotonicity. We further establish a novel connection between the structured optimal control and the external positivity of the costate dynamics. These results provide a rigorous theoretical foundation for heuristic charging strategies and explain the efficiency of optimization-free algorithms.

math.OC↗

arXiv2025

A Hierarchical Surrogate Model for Efficient Multi-Task Parameter Learning in Closed-Loop Control

Many control problems require repeated tuning and adaptation of controllers across distinct closed-loop tasks, where data efficiency and adaptability are critical. We propose a hierarchical Bayesian optimization (BO) framework that is tailored to efficient controller parameter learning in sequential decision-making and control scenarios for distinct tasks. Instead of treating the closed-loop cost as a black-box, our method exploits structural knowledge of the underlying problem, consisting of a dynamical system, a control law, and an associated closed-loop cost function. We construct a hierarchical surrogate model using Gaussian processes that capture the closed-loop state evolution under different parameterizations, while the task-specific weighting and accumulation into the closed-loop cost are computed exactly via known closed-form expressions. This allows knowledge transfer and enhanced data efficiency between different closed-loop tasks. The proposed framework retains sublinear regret guarantees on par with standard black-box BO, while enabling multi-task or transfer learning. Simulation experiments with model predictive control demonstrate substantial benefits in both sample efficiency and adaptability when compared to purely black-box BO approaches.

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arXiv2025

Safe and High-Performance Learning of Model Predicitve Control using Kernel-Based Interpolation

We present a method that allows efficient and safe approximation of model predictive controllers using kernel interpolation. Since the computational complexity of the approximating function scales linearly with the number of data points, we propose to use a scoring function which chooses the most promising data. To further reduce the complexity of the approximation, we restrict our considerations to the set of closed-loop reachable states. That is, the approximating function only has to be accurate within this set. This makes our method especially suited for systems, where the set of initial conditions is small. In order to guarantee safety and high performance of the designed approximated controller, we use reachability analysis based on Monte Carlo methods.

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arXiv2025

Safe Physics-Informed Machine Learning for Dynamics and Control

This tutorial paper focuses on safe physics-informed machine learning in the context of dynamics and control, providing a comprehensive overview of how to integrate physical models and safety guarantees. As machine learning techniques enhance the modeling and control of complex dynamical systems, ensuring safety and stability remains a critical challenge, especially in safety-critical applications like autonomous vehicles, robotics, medical decision-making, and energy systems. We explore various approaches for embedding and ensuring safety constraints, including structural priors, Lyapunov and Control Barrier Functions, predictive control, projections, and robust optimization techniques. Additionally, we delve into methods for uncertainty quantification and safety verification, including reachability analysis and neural network verification tools, which help validate that control policies remain within safe operating bounds even in uncertain environments. The paper includes illustrative examples demonstrating the implementation aspects of safe learning frameworks that combine the strengths of data-driven approaches with the rigor of physical principles, offering a path toward the safe control of complex dynamical systems.

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arXiv2025

Efficient Learning of Vehicle Controller Parameters via Multi-Fidelity Bayesian Optimization: From Simulation to Experiment

Parameter tuning for vehicle controllers remains a costly and time-intensive challenge in automotive development. Traditional approaches rely on extensive real-world testing, making the process inefficient. We propose a multi-fidelity Bayesian optimization approach that efficiently learns optimal controller parameters by leveraging both low-fidelity simulation data and a very limited number of real-world experiments. Our approach significantly reduces the need for manual tuning and expensive field testing while maintaining the standard two-stage development workflow used in industry. The core contribution is the integration of an auto-regressive multi-fidelity Gaussian process model into Bayesian optimization, enabling knowledge transfer between different fidelity levels without requiring additional low-fidelity evaluations during real-world testing. We validate our approach through both simulation studies and realworld experiments. The results demonstrate that our method achieves high-quality controller performance with only very few real-world experiments, highlighting its potential as a practical and scalable solution for intelligent vehicle control tuning in industrial applications.

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arXiv2025

A Modular Energy Aware Framework for Multicopter Modeling in Control and Planning Applications

Unmanned aerial vehicles (UAVs), especially multicopters, have recently gained popularity for use in surveillance, monitoring, inspection, and search and rescue missions. Their maneuverability and ability to operate in confined spaces make them particularly useful in cluttered environments. For advanced control and mission planning applications, accurate and resource-efficient modeling of UAVs and their capabilities is essential. This study presents a modular approach to multicopter modeling that considers vehicle dynamics, energy consumption, and sensor integration. The power train model includes detailed descriptions of key components such as the lithium-ion battery, electronic speed controllers, and brushless DC motors. Their models are validated with real test flight data. In addition, sensor models, including LiDAR and cameras, are integrated to describe the equipment often used in surveillance and monitoring missions. The individual models are combined into an energy-aware multicopter model, which provide the basis for a companion study on path planning for unmanned aircaft system (UAS) swarms performing search and rescue missions in cluttered and dynamic environments. The flexible modeling approach enables easy description of different UAVs in a heterogeneous UAS swarm, allowing for energy-efficient operations and autonomous decision making for a reliable mission performance.

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arXiv2025

Energy Aware and Safe Path Planning for Unmanned Aircraft Systems

This paper proposes a path planning algorithm for multi-agent unmanned aircraft systems (UASs) to autonomously cover a search area, while considering obstacle avoidance, as well as the capabilities and energy consumption of the employed unmanned aerial vehicles. The path planning is optimized in terms of energy efficiency to prefer low energy-consuming maneuvers. In scenarios where a UAS is low on energy, it autonomously returns to its initial position for a safe landing, thus preventing potential battery damage. To accomplish this, an energy-aware multicopter model is integrated into a path planning algorithm based on model predictive control and mixed integer linear programming. Besides factoring in energy consumption, the planning is improved by dynamically defining feasible regions for each UAS to prevent obstacle corner-cutting or over-jumping.

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