arXiv subjects

Thomas Berger

Publications and source records attributed to Thomas Berger.

At least 19 recordsLinked to original sources

arXiv2026

Funnel MPC for port-Hamiltonian systems

Port-Hamiltonian systems are an energy-based modelling formalism, that has strong ties to the physical models and allows interconnection of systems. Funnel MPC, a Model Predictive Control (MPC) scheme, allows for output tracking with prescribed error bounds. Earlier works focused on systems with stable internal dynamics, which typically excludes port-Hamiltonian systems. We introduce a modified stage cost design that takes into account the port-Hamiltonian structure of the system and allows deactivation of the funnel cost. We show initial and recursive feasibility for a class of port-Hamiltonian systems with relative degree one including unstable internal dynamics.

math.OC↗

arXiv2026

Event-Triggered Funnel Control for Output Reference Tracking of Unknown Nonlinear Systems

We propose an event-triggered zero-order hold implementation of the funnel controller for output reference tracking of unknown nonlinear systems. The control input is updated only when the deviation between the current and the last transmitted input exceeds a prescribed threshold, reducing the number of input updates while maintaining closed-loop performance guarantees by incorporating an auxiliary integral state to compensate for the error introduced by the zero-order-hold input. We establish a uniform lower bound on the inter-event intervals excluding Zeno behavior, and derive a growth condition on the nonlinear dynamics that ensures global existence of the solution for arbitrary, predefined sampling schedules. The theoretical results are illustrated by numerical simulations.

math.OC↗

arXiv2026

Safe Platooning under Input Constraints with Link-Wise Velocity String Stability

We propose a decentralized controller for vehicle platoons with different braking and propulsion limits. The method uses only local distance and velocity measurements and requires neither online optimization nor exact vehicle parameters. The design combines a braking-distance safety margin with an adaptive funnel that relaxes the spacing requirement during propulsion saturation. A standstill mechanism prevents backward motion and supports stop-and-go operation. Under explicit uniform conditions on the vehicle parameters, controller settings, and initial states, we prove that closed-loop solutions exist for all time, collisions are avoided, and input limits are satisfied. Moreover, each follower tracks its predecessor's velocity range with gain one, up to an explicit additive offset determined by the funnel width and the braking-distance term. This bound establishes link-wise velocity string stability. Both the offset and the bounds on speeds and spacing errors are independent of vehicle index and platoon length. Simulations with 2 to 100 followers illustrate safety and bounded velocity deviations under disturbances and actuator limits.

eess.SY↗

arXiv2026

Funnel-Precompensated Disturbance Observer for Uncertain Minimum-Phase SISO Linear Systems of Arbitrary Relative Degree

Disturbance observers (DOBs) recover nominal behavior, but fast filters risk peaking. We propose a funnel-precompensated DOB for uncertain minimum-phase single-input single-output linear systems of known relative degree. A stable-factor residual yields a minimum-phase channel. At relative degree two, gain conditions require positive plant high-frequency gains and one positive common design gain; for higher degrees, the common-design result also uses a plant-gain interval and mismatch condition. Global boundedness, practical nominal-output recovery, and open-funnel initialization are established.

eess.SY↗

arXiv2026

Euler Time-Discretization of Funnel-Controlled Dynamics

We analyze explicit and implicit Euler discretizations of the continuous-time closed-loop dynamics generated by a funnel controller for a fully actuated nonlinear full-state system of relative degree one with scalar positive input gain. A quantitative continuous-time funnel margin provides the compactness and regularity bounds needed for the error analysis. For explicit Euler, a computable upper step-size threshold guarantees a global nodewise distance from the funnel boundary. We show that first-order convergence holds on finite time horizons and, under a~dissipativity condition (a~one-sided Lipschitz bound on the plant dominated by the funnel damping), uniformly in time. For implicit Euler, an admissible update exists for every step size and every trajectory initialized in the funnel retains a step-size-independent nodal margin. Under dissipativity, the admissible root is unique for every step size, the discrete flow is contractive, and the first-order error bound is uniform in time.

math.OC↗

arXiv2026

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↗

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

Optimal Bias Potentials via Ergodic Optimal Control and Generator Learning

We investigate the computation of optimal bias potentials for accelerating transitions between metastable states and for computation of equilibrium properties in molecular dynamics simulations. We formulate optimal biasing as an ergodic optimal control problem (OCP), which can be recast as a linear eigenvalue problem for the infinitesimal generator of the unbiased dynamics. We demonstrate that data-driven learning methods for the generator enable reliable solution of the OCP, computation of biasing potentials, extraction of equilibrium properties, and acceleration of state transitions. We also explore the relation of the control problem to coarse grained representations and learning of coarse grained dynamics.

physics.comp-ph↗

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 of arbitrary relative degree. We propose a novel derivative-free extension of funnel control based on a set of auxiliary 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 validated by a numerical example.

math.OC↗

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

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↗

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↗

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

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↗

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

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↗