arXiv subjects

Thomas Berger

Publications and source records attributed to Thomas Berger.

At least 37 records · Page 2Linked to original sources

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

Asymptotic tracking by funnel control with internal models

Funnel control achieves output tracking with guaranteed tracking performance for unknown systems and arbitrary reference signals. In particular, the tracking error is guaranteed to satisfy time-varying error bounds for all times (it evolves in the funnel). However, convergence to zero cannot be guaranteed, but the error often stays close to the funnel boundary, inducing a comparatively large feedback gain. This has several disadvantages (e.g. poor tracking performance and sensitivity to noise due to the underlying high-gain feedback principle). In this paper, therefore, the usually known reference signal is taken into account during funnel controller design, i.e. we propose to combine the well-known internal model principle with funnel control. We focus on linear systems with linear reference internal models and show that under mild adjustments of funnel control, we can achieve asymptotic tracking for a whole class of linear systems (i.e. without relying on the knowledge of system parameters).

math.OC↗

arXiv2024

Funnel MPC for nonlinear systems with arbitrary relative degree

The Model Predictive Control (MPC) scheme Funnel MPC enables output tracking of smooth reference signals with prescribed error bounds for nonlinear multi-input multi-output systems with stable internal dynamics. Earlier works achieved the control objective for system with relative degree restricted to one or incorporated additional feasibility constraints in the optimal control problem. Here we resolve these limitations by introducing a modified stage cost function relying on a weighted sum of the tracking error derivatives. The weights need to be sufficiently large and we state explicit lower bounds. Under these assumptions we are able to prove initial and recursive feasibility of the novel Funnel MPC scheme for systems with arbitrary relative degree - without requiring any terminal conditions, a sufficiently long prediction horizon or additional output constraints.

math.OC↗

arXiv2023

Robust Funnel Model Predictive Control for output tracking with prescribed performance

We propose a novel robust Model Predictive Control (MPC) scheme for nonlinear multi-input multi-output systems of relative degree one with stable internal dynamics. The proposed algorithm is a combination of funnel MPC, i.e., MPC with a particular stage cost, and the model-free adaptive funnel controller. The new robust funnel MPC scheme guarantees output tracking of reference signals within prescribed performance bounds -- even in the presence of unknown disturbances and a structural model-plant mismatch. We show initial and recursive feasibility of the proposed control scheme without imposing terminal conditions or any requirements on the prediction horizon. Moreover, we allow for model updates at runtime. To this end, we propose a proper initialization strategy, which ensures that recursive feasibility is preserved. Finally, we validate the performance of the proposed robust MPC scheme by simulations.

math.OC↗

arXiv2023

Experimental validation for the combination of funnel control with a feedforward control strategy

Current engineering design trends, such as light-weight machines and humanmachine-interaction, often lead to underactuated systems. Output trajectory tracking of such systems is a challenging control problem. Here, we use a twodesign-degree of freedom control approach by combining funnel feedback control with feedforward control based on servo-constraints. We present experimental results to verify the approach and demonstrate that the addition of a feedforward controller mitigates drawbacks of the funnel controller. We also present new experimental results for the real-time implementation of a feedforward controller based on servo-constraints on a minimum phase system.

math.OC↗

arXiv2023

Funnel control of linear systems with arbitrary relative degree under output measurement losses

We consider tracking control of linear minimum phase systems with known arbitrary relative degree which are subject to possible output measurement losses. We provide a control law which guarantees the evolution of the tracking error within a (shifted) prescribed performance funnel whenever the output signal is available. The result requires a maximal duration of measurement losses and a minimal time of measurement availability, which both strongly depend on the internal dynamics of the system, and are derived explicitly. The controller is illustrated by a simulation of a mass-on-car system.

math.OC↗

arXiv2023

Maneuvering tracking algorithm for reentry vehicles with guaranteed prescribed performance

This paper presents a prescribed performance-based tracking control strategy for the atmospheric reentry flight of space vehicles subject to rapid maneuvers during flight mission. A time-triggered non-monotonic performance funnel is proposed with the aim of constraints violation avoidance in the case of sudden changes of the reference trajectory. Compared with traditional prescribed performance control methods, the novel funnel boundary is adaptive with respect to the reference path and is capable of achieving stability under disturbances. A recursive control structure is introduced which does not require any knowledge of specific system parameters. By a stability analysis we show that the tracking error evolves within the prescribed error margin under a condition which represents a trade-off between the reference signal and the performance funnel. The effectiveness of the proposed control scheme is verified by simulations.

math.OC↗

arXiv2023

Funnel Control for Langevin Dynamics

We study tracking control for stochastic differential equations of Langevin type and describe a new conceptual approach to the sampling problem for those systems. The objective is to guarantee the evolution of the mean value in a prescribed performance funnel around a given sufficiently smooth reference signal. To achieve this objective we design a novel funnel controller and show its feasibility under certain structural conditions on the potential energy. The control design does not require any specific knowledge of the shape of the potential energy. We illustrate the results by a numerical simulation for a double-well potential.

math.OC↗

arXiv2023

Input-constrained funnel control of nonlinear systems

We study tracking control for uncertain nonlinear multi-input, multi-output systems modelled by $r$-th order functional differential equations (encompassing systems with arbitrary strict relative degree) in the presence of input constraints. The objective is to guarantee the evolution of the tracking error within a performance funnel with prescribed asymptotic shape (thus achieving desired transient and asymptotic accuracy objectives), for any sufficiently smooth reference signal. We design a novel funnel controller which, in order to satisfy the input constraints, contains a dynamic component which widens the funnel boundary whenever the input saturation is active. This design is model-free, of low-complexity and extends earlier funnel control approaches. We present a simulation where the controller is compared to these approaches.

math.OC↗

arXiv2023

Existence Conditions for Functional ODE Observer Design of Descriptor Systems Revisited

This paper is devoted to the problem of designing functional observers for linear time-invariant (LTI) descriptor systems. The observers are realized by using state-space systems governed by ordinary differential equations (ODEs). Available existence results for functional ODE observers in the literature are extended by introducing new and milder sufficient conditions. These conditions are purely algebraic and provided directly in terms of the system coefficient matrices. The proposed observer has an order less than or equal to the dimension of the functional vector to be estimated. The observer parameter matrices are obtained by using simple matrix theory, and the design algorithm is illustrated by numerical examples.

math.OC↗

arXiv2023

Partial detectability and generalized functional observer design for linear descriptor systems

This paper studies linear time-invariant descriptor systems which are not necessarily regular. We introduce the notion of partial detectability and characterize this concept by means of a simple rank criterion involving the system coefficient matrices. Three particular cases of this characterization are discussed in detail. Furthermore, we show that partial detectability is necessary for the existence of a generalized functional observer, but not sufficient. We identify a condition which together with partial detectability gives sufficiency.

math.OC↗

arXiv2023

Edge-wise funnel output synchronization of heterogeneous agents with relative degree one

When a group of heterogeneous node dynamics are diffusively coupled with a high coupling gain, the group exhibits a collective emergent behavior which is governed by a simple algebraic average of the node dynamics called the blended dynamics. This finding has been utilized for designing heterogeneous multi-agent systems by building the desired blended dynamics first and then splitting it into the node dynamics. However, to compute the magnitude of the coupling gain, each agent needs to know global information such as the number of participating nodes, the graph structure, and so on, which prevents a fully decentralized design of the node dynamics in conjunction with the coupling laws. To resolve this issue, the idea of funnel control, which is a method for adaptive gain selection, can be exploited for a node-wise coupling, but the price to pay is that the collective emergent behavior is no longer governed by a simple average of the node dynamics. Our analysis reveals that this drawback can be avoided by an edge-wise design premise, which is the idea that we present in this paper. After all, we gain benefits such as a fully decentralized design without global information, collective emergent behavior being governed by the blended dynamics, and the plug-and-play operation based on edge-wise handshaking between two nodes.

eess.SY↗

arXiv2022

A Jordan-like decomposition for linear relations in finite-dimensional spaces

A square matrix $A$ has the usual Jordan canonical form that describes the structure of $A$ via eigenvalues and the corresponding Jordan blocks. If $A$ is a linear relation in a finite-dimensional linear space ${\mathfrak H}$ (i.e., $A$ is a linear subspace of ${\mathfrak H} \times {\mathfrak H}$ and can be considered as a multivalued linear operator), then there is a richer structure. In addition to the classical Jordan chains (interpreted in the Cartesian product ${\mathfrak H} \times {\mathfrak H}$), there occur three more classes of chains: chains starting at zero (the chains for the eigenvalue infinity), chains starting at zero and also ending at zero (the singular chains), and chains with linearly independent entries (the shift chains). These four types of chains give rise to a direct sum decomposition (a Jordan-like decomposition) of the linear relation $A$. In this decomposition there is a completely singular part that has the extended complex plane as eigenvalues; a usual Jordan part that corresponds to the finite proper eigenvalues; a Jordan part that corresponds to the eigenvalue $\infty$; and a multishift, i.e., a part that has no eigenvalues at all. Furthermore, the Jordan-like decomposition exhibits a certain uniqueness, closing a gap in earlier results. The presentation is purely algebraic, only the structure of linear spaces is used. Moreover, the presentation has a uniform character: each of the above types is constructed via an appropriately chosen sequence of quotient spaces. The dimensions of the spaces are the Weyr characteristics, which uniquely determine the Jordan-like decomposition of the linear relation.

math.FA↗

arXiv2022

Funnel MPC with feasibility constraints for nonlinear systems with arbitrary relative degree

We study tracking control for nonlinear systems with known relative degree and stable internal dynamics by the recently introduced technique of Funnel MPC. The objective is to achieve the evolution of the tracking error within a prescribed performance funnel. We propose a novel stage cost for Funnel MPC, extending earlier designs to the case of arbitrary relative degree, and show that the control objective as well as initial and recursive feasibility are always achieved - without requiring any terminal conditions or a sufficiently long prediction horizon. We only impose an additional feasibility constraint in the optimal control problem.

math.OC↗

arXiv2022

Funnel MPC for nonlinear systems with relative degree one

We show that Funnel MPC, a novel Model Predictive Control (MPC) scheme, allows tracking of smooth reference signals with prescribed performance for nonlinear multi-input multi-output systems of relative degree one with stable internal dynamics. The optimal control problem solved in each iteration of Funnel MPC resembles the basic idea of penalty methods used in optimization. To this end, we present a new stage cost design to mimic the high-gain idea of (adaptive) funnel control. We rigorously show initial and recursive feasibility of Funnel MPC without imposing terminal conditions or other requirements like a sufficiently long prediction horizon.

math.OC↗

arXiv2022

Machine Learning Approaches to Solar-Flare Forecasting: Is Complex Better?

Recently, there has been growing interest in the use of machine-learning methods for predicting solar flares. Initial efforts along these lines employed comparatively simple models, correlating features extracted from observations of sunspot active regions with known instances of flaring. Typically, these models have used physics-inspired features that have been carefully chosen by experts in order to capture the salient features of such magnetic field structures. Over time, the sophistication and complexity of the models involved has grown. However, there has been little evolution in the choice of feature sets, nor any systematic study of whether the additional model complexity is truly useful. Our goal is to address these issues. To that end, we compare the relative prediction performance of machine-learning-based, flare-forecasting models with varying degrees of complexity. We also revisit the feature set design, using topological data analysis to extract shape-based features from magnetic field images of the active regions. Using hyperparameter training for fair comparison of different machine-learning models across different feature sets, we show that simpler models with fewer free parameters \textit{generally perform better than more-complicated models}, ie., powerful machinery does not necessarily guarantee better prediction performance. Secondly, we find that \textit{abstract, shape-based features contain just as much useful information}, for the purposes of flare prediction, as the set of hand-crafted features developed by the solar-physics community over the years. Finally, we study the effects of dimensionality reduction, using principal component analysis, to show that streamlined feature sets, overall, perform just as well as the corresponding full-dimensional versions.

astro-ph.SR↗