arXiv subjects

Thomas Berger

Publications and source records attributed to Thomas Berger.

At least 19 recordsLinked to original sources

arXiv2026

Distance-Based Formation Control with Prescribed Performance for Higher-Order Multi-Agent Systems

We consider distributed distance-based formation control with prescribed transient performance for multi-agent systems modeled by unknown nonlinear dynamics of relative degree greater than one. We introduce a virtual leader whose trajectory is tracked with prescribed transient behavior by a designated subset of agents. The undirected communication graph is either a tree graph or a minimally and infinitesimally rigid graph. In the latter case, we further consider the objective of centroid tracking. In each setting, a distributed and model-free control law is developed, and we establish the satisfaction of the prescribed funnel constraints on the formation and tracking errors, and boundedness of all closed-loop signals. Numerical simulations illustrate the effectiveness of the proposed control laws.

math.OC↗

arXiv2026

Port-Hamiltonian modelling of coupled rigid/flexible multibody systems

We develop a port-Hamiltonian framework for coupled rigid/flexible multibody systems. The rigid dynamics may be nonlinear and subject to configuration and velocity constraints, while the flexible components are described by linear port-Hamiltonian partial differential equations on one-dimensional spatial domains. The subsystems interact through boundary or distributed ports. On the flexible side, the differential operator and its domain remain fixed, whereas state dependence enters only through finite-dimensional coupling components of the Dirac structure. We show that, under a natural surjectivity condition, the port-Hamiltonian interconnection with a modulated Dirac structure of a finite-dimensional rigid subsystem again yields a modulated Dirac structure. The Hamiltonians of the subsystems add, while the internal coupling powers cancel. The framework is illustrated by a planar moving Euler--Bernoulli beam and a slider--crank mechanism with a flexible connecting member.

math.DS↗

arXiv2026

A model-free approach to control barrier functions for higher-order systems

Control barrier functions (CBFs) are a widely applied modular tool to ensure safe operation of nonlinear dynamical control systems. However, for their construction accurate knowledge of the system dynamics is typically needed. This requirement was recently alleviated for relative-degree-one systems using techniques from prescribed performance control (PPC) or funnel control (FC). This article extends the model-free CBF design to nonlinear systems of arbitrary relative degree. Moreover, we show with a simple example that a straightforward extension of existing results for relative-degree-one systems fails. Instead, we utilize novel techniques from funnel control to characterize a subset of the controls satisfying a CBF condition without requiring a dynamic model or state measurement. Finally, we demonstrate the applicability of our results on a seven degrees of freedom robotic manipulator with relative degree two.

eess.SY↗

arXiv2026

Funnel control with input filter for nonlinear systems with arbitrary relative degree

This paper addresses output reference tracking with prescribed transient performance for unknown nonlinear multi-input multi-output systems with arbitrary relative degree. We propose a novel derivative-free extension of funnel control based on a collection of filter variables that estimate the output derivatives. The resulting controller ensures that the tracking error evolves within prescribed performance bounds, while avoiding differentiation of the output signal and maintaining a simple structure with only a small number of tuning parameters. The effectiveness of the proposed approach is illustrated by a numerical example.

math.OC↗

arXiv2026

Analysis and funnel control for nonlinear drill strings

We study the output tracking problem for a vertically driven drill string system described by a nonlinear boundary-coupled PDE-ODE model. Solvability analysis of the drill string model is achieved by first casting the model in an abstract boundary value problem involving set-valued operators on an appropriate Hilbert space. The governing equation here consists of evolution and the damping part. Existence of solutions is established within the framework of maximal monotone operators where one first proves that the evolution operator is a linear skew-adjoint operator and the distributed damping term is a Nemytskii relation which is then proven to be maximal monotone. Maximal monotonicity of the combined operator is then a consequence of Rockafellar's theorem. Furthermore, we propose a novel funnel control design that ensures the angular velocity of the drill bit follows a dynamically adjusted reference trajectory, while the tracking error remains confined within a pre-specified performance funnel. The reference adjustment mechanism adapts in response to large wave traveling times that may cause performance degradation. The corresponding feasibility result is illustrated by some simulations.

math.OC↗

arXiv2026

Accurate and Reliable Uncertainty Estimates for Deterministic Predictions Extensions to Under and Overpredictions

Computational models support high-stakes decisions across engineering and science, and practitioners increasingly seek probabilistic predictions to quantify uncertainty in such models. Existing approaches generate predictions either by sampling input parameter distributions or by augmenting deterministic outputs with uncertainty representations, including distribution-free and distributional methods. However, sampling-based methods are often computationally prohibitive for real-time applications, and many existing uncertainty representations either ignore input dependence or rely on restrictive Gaussian assumptions that fail to capture asymmetry and heavy-tailed behavior. Therefore, we extend the ACCurate and Reliable Uncertainty Estimate (ACCRUE) framework to learn input-dependent, non-Gaussian uncertainty distributions, specifically two-piece Gaussian and asymmetric Laplace forms, using a neural network trained with a loss function that balances predictive accuracy and reliability. Through synthetic and real-world experiments, we show that the proposed approach captures an input-dependent uncertainty structure and improves probabilistic forecasts relative to existing methods, while maintaining flexibility to model skewed and non-Gaussian errors.

cs.CE↗

arXiv2026

Distributed partial state estimation for linear state-space systems

This study is concerned with the problem of partial state estimation for linear time-invariant (LTI) distributed state-space systems. A necessary and sufficient condition is established in terms of a simple rank criterion involving the system coefficient matrices, provided the communication graph is either directed, balanced and strongly connected or undirected and connected. The estimator parameter matrices are obtained by simple matrix theory. Finally, a numerical example demonstrates the feasibility and effectiveness of the proposed theoretical results and design algorithm.

math.OC↗

arXiv2026

Data-Based Analysis of Relative Degree and Zero Dynamics in Linear Systems

Data-driven control offers a powerful alternative to traditional model-based methods, particularly when accurate system models are unavailable or prohibitively complex. While existing data-driven control methods primarily aim to construct controllers directly from measured data, our approach uses the available data to assess fundamental system-theoretic properties. This allows the informed selection of suitable control strategies without explicit model identification. We provide data-based conditions characterizing the (vector) relative degree and the stability of the zero dynamics, which are critical for ensuring proper performance of modern controllers. Our results cover both single- and multi-input/output settings of discrete-time linear systems. We further show how a continuous-time system can be reconstructed from three sampling discretizations obtained via Zero-order Hold at suitable sampling times, thus allowing the extension of the results to the combined data collected from these discretizations. All results can be applied directly to observed data sets using the proposed algorithms.

eess.SY↗

arXiv2025

Some Remarks on Positive/Negative Feedback

In the context of linear control systems, a commonly-held intuition is that negative and positive feedback cannot both be stability enhancing. The canonical linear prototype is the scalar system $\dot x=u$ which, under negative linear feedback $u=-kx$ ($k >0$) is exponentially stable for all $k >0 $, whereas the lack of exponential instability of the (marginally stable) uncontrolled system is amplified by positive feedback $u=kx$ ($k >0)$. By contrast, for nonlinear systems it is shown, by example, that this intuitive dichotomy may fail to hold.

math.OC↗

arXiv2025

Prescribed Performance Control of Uncertain Higher Relative Degree Nonlinear Systems in the Presence of Delays

We propose a novel feedback controller for a class of uncertain higher relative degree nonlinear systems, subject to delays in both state measurement and control input signals. Building on the prescribed performance control framework, a delay-dependent performance correction mechanism is introduced to ensure the boundedness of all signals in the closed-loop and to keep the output tracking error strictly within a dynamically adjusted performance envelope. This mechanism adapts in response to large delays that may cause performance degradation. In the absence of delays, the correction term vanishes, and the controller recovers the nominal (user-defined) performance envelope. The effectiveness of the proposed approach is validated through simulation studies.

math.OC↗

arXiv2025

An improved input-constrained funnel controller for nonlinear systems

We present an improvement of a recent funnel controller design for uncertain nonlinear multi-input, multi-output systems modeled by higher order functional differential equations in the presence of input constraints. The objective is to guarantee the evolution of the tracking error within a performance funnel with prescribed desired shape for the case of inactive saturation. Compared to its precursor, controller complexity is significantly reduced, much fewer design parameters are involved and simulations exhibit a superior performance.

math.OC↗

arXiv2025

On Model Predictive Funnel Control with Equilibrium Endpoint Constraints

We propose model predictive funnel control, a novel model predictive control (MPC) scheme building upon recent results in funnel control. The latter is a high-gain feedback methodology that achieves evolution of the measured output within predefined error margins. The proposed method dynamically optimizes a parameter-dependent error boundary in a receding-horizon manner, thereby combining prescribed error guarantees from funnel control with the predictive advantages of MPC. On the one hand, this approach promises faster optimization times due to a reduced number of decision variables, whose number does not depend on the horizon length. On the other hand, the continuous feedback law improves the robustness and also explicitly takes care of the inter-sampling behavior. We focus on proving stability by leveraging results from MPC stability theory with terminal equality constraints. Moreover, we rigorously show initial and recursive feasibility.

math.OC↗

arXiv2025

A model-free approach to control barrier functions using funnel control

Control barrier functions (CBFs) are a popular approach to design feedback laws that achieve safety guarantees for nonlinear systems. The CBF-based controller design relies on the availability of a model to select feasible inputs from the set of CBF-based controls. In this paper, we develop a model-free approach to design CBF-based control laws, eliminating the need for knowledge of system dynamics or parameters. Specifically, we address safety requirements characterized by a time-varying distance to a reference trajectory in the output space and construct a CBF that depends only on the measured output. Utilizing this particular CBF, we determine a subset of CBF-based controls without relying on a model of the dynamics by using techniques from funnel control. The latter is a model-free high-gain adaptive control methodology, which achieves tracking guarantees via reactive feedback. In this paper, we discover and establish a connection between the modular controller synthesis via zeroing CBFs and model-free reactive feedback. The theoretical results are illustrated by a numerical simulation.

math.OC↗

arXiv2025

Port-Hamiltonian modeling of rigid multibody systems

We employ a port-Hamiltonian approach to model nonlinear rigid multibody systems subject to both position and velocity constraints. Our formulation accommodates Cartesian and redundant coordinates, respectively, and captures kinematic as well as gyroscopic effects. The resulting equations take the form of nonlinear differential-algebraic equations that inherently preserve an energy balance. We show that the proposed class is closed under interconnection, and we provide several examples to illustrate the theory.

math.DS↗

arXiv2025

Nowcasting Solar Energetic Particle Events for Mars Missions

In addition to the omnipresent Galactic Cosmic Rays (GCRs), sudden solar energetic particle (SEP) events present considerable health hazards for manned space missions. These events not only contribute to an increased long-term cancer risk, but can, in extreme cases, cause acute radiation syndromes. Forecasting their imminent occurrence could significantly reduce radiation exposure by warning astronauts to move to shelter. However, all currently available tools are primarily designed for the Earth or Earth-Moon system, which limits their applicability to future Mars missions. To address this, we developed a nowcasting system for SEP events applicable in deep space and on the Martian surface, which serves as a reliable last-resort backup when forecasts fail. The methodology of this system is based on dose rates measured by the Radiation Assessment Detector (RAD) onboard the Mars Science Laboratory (MSL), which recorded 5 SEP events during the seven-month flight to Mars and 16 since its landing on Mars on August 6, 2012. An SEP event is triggered, and an astronaut is warned as soon as dose rates exceed the omnipresent background level by at least 25%. This approach suggests that our system can provide astronauts with at least 30 minutes to avoid both peak radiation exposure and the majority of the cumulative dose from SEP events. Our nowcasting system is robust, easily implementable in real-life scenarios, and achieves a near-zero false alarm rate both in deep space and on the Martian surface.

physics.space-ph↗

arXiv2024

Effective dose equivalent estimation for humans on Mars

Exposure to cosmic radiation is a major concern in space exploration. On the Martian surface, a complex radiation field is present, formed by a constant influx of galactic cosmic radiation and the secondary particles produced by their interaction with the planet's atmosphere and regolith. In this work, a Martian environment model was developed using MCNP6 following the guidelines of the 1st Mars Space Radiation Modeling Workshop. The accuracy of the model was tested by comparing particle spectra and dose rate results with other model results and measurements from the Radiation Assessment Detector (RAD) onboard the Curiosity rover, taken between November 15, 2015, and January 15, 2016. The ICRP's voxel-type computational phantoms were then implemented into the code. Organ dose and effective dose equivalent were assessed for the same time period. The viability of a mission on the surface of Mars for extended periods of time under the assumed conditions was here investigated.

physics.space-ph↗

arXiv2024

Partial Causal Detectability of Linear Descriptor Systems and Existence of Functional ODE Estimators

This paper studies the problem of state estimation for linear time-invariant descriptor systems in their most general form. The estimator is a system of ordinary differential equations (ODEs). We introduce the notion of partial causal detectability and characterize this concept by means of a simple rank criterion involving the system coefficient matrices. Also, several equivalent characterizations for partial causal detectability are established. In addition, we prove that partial causal detectability is equivalent to the existence of functional ODE estimators. A numerical example is given to validate the theoretical results.

math.OC↗

arXiv2024

String stability and guaranteed safety via funnel cruise control for vehicle platoons

We study decentralized control strategies for platoons of autonomous vehicles with heterogeneous and nonlinear dynamics. Based on ideas from funnel control, we present a novel decentralized control algorithm which is able to guarantee a safety distance between any two vehicles, a good traffic flow and it achieves string stability of the controlled platoon. We illustrate the performance of the controller by simulations of two extreme scenarios.

math.OC↗