arXiv subjects

Michael Stolz

Publications and source records attributed to Michael Stolz.

18 recordsLinked to original sources

arXiv2025

A nonlinear dead-time compensation method for path tracking control

In the realm of autonomous vehicle technologies and advanced driver assistance systems, precise and reliable path tracking controllers are vital for safe and efficient navigation. However the presence of dead time in the vehicle control systems poses a challenge to real-world systems. Input and output delays are caused by factors like sensor processing and mechanical response and can range up to a few hundred milliseconds. This chapter addresses the problem of dead time in path tracking control and proposes a method to compensate the dead time. The proposed solution involves a nonlinear prediction model, in a structure similar to the Smith predictor, but incorporating the kinematic behavior of the vehicle plant system. The implementation avoids numeric integration or optimization, enabling a fast execution. Simulation tests with various controllers and disturbances, including dead-time uncertainty, demonstrate the efficacy of the dead-time compensation method. Results indicate improved control performance in all tested scenarios.

eess.SY↗

arXiv2023

Multi-objective path tracking control for car-like vehicles with differentially bounded n-smooth output

When designing path tracking controllers for car-like vehicles, two main aspects are the tracking performance and the characteristics of the actuation signal. Our work bases on an existing variable structure controller that was designed with the geometrically optimal solution of a Dubins car, but with chattering on the output. In this contribution, we extend this approach to achieve an actuation signal that is n-smooth and differentially bounded. While the global stability under matched disturbances is maintained, the finite time reaching behavior is exchanged for asymptotic convergence. With the $n$-smooth output, n new parameters are introduced, weighing the control characteristics between the tracking performance and the magnitude of the steering angles derivatives. The controller is also evaluated in simulation, demonstrating the tuning capabilities, as well as the reaching and tracking behavior. The main contribution of this work is a control law designed to produce a smooth steering angle with implicit satisfaction of bounds on its derivatives.

eess.SY↗

arXiv2023

Dual-Weight Particle Filter for Radar-Based Dynamic Bayesian Grid Maps

Through constant improvements in recent years radar sensors have become a viable alternative to lidar as the main distancing sensor of an autonomous vehicle. Although robust and with the possibility to directly measure the radial velocity, it brings it's own set of challenges, for which existing algorithms need to be adapted. One core algorithm of a perception system is dynamic occupancy grid mapping, which has traditionally relied on lidar. In this paper we present a dual-weight particle filter as an extension for a Bayesian occupancy grid mapping framework to allow to operate it with radar as its main sensors. It uses two separate particle weights that are computed differently to compensate that a radial velocity measurement in many situations is not able to capture the actual velocity of an object. We evaluate the method extensively with simulated data and show the advantages over existing single weight solutions.

cs.RO↗

arXiv2022

Coulomb actuated microbeams: A Chebyshev-Edgeworth approach to highly efficient lumped parameter models

In a previous publication we demonstrated that the stable and unstable equilibrium states of prismatic Coulomb actuated Euler-Bernoulli micro-beams, clamped at both ends, can successfully be simulated combining finite element analysis (FEM) with continuation methods. Simulation results were experimentally scrutinised by combining direct optical observations with a modal analysis regarding Euler-Bernoulli eigenmodes. Experiment and simulation revealed convincing evidence for the possibility of modelling the physics of such a micro-beam by means of lumped parameter models involving only a single degree of freedom, the Euler-Bernoulli zero mode. In this paper we present the corresponding analytical single degree of freedom lumped parameter model (LPM). This comprehensive model demonstrates the impact of the beam bending on the nature of the Coulomb singularity, allows for an easy and accurate computation of the pull-in voltage in the presence of stress stiffening and is apt for efficient frequency response computations. Our method to derive the zero-mode LPM is based on a Chebyshev-Edgeworth type method as is common in analytical probability theory. While used here for a very particular purpose, this novel approach to non-linear dynamic systems has a much broader scope. It is apt to analyse different boundary conditions, electrostatic fringe field corrections and squeeze film damping, to name a few applications.

physics.app-ph↗

arXiv2021

JTrack: A Digital Biomarker Platform for Remote Monitoring in Neurological and Psychiatric Diseases

Objective: Health-related data being collected by smartphones offer a promising complementary approach to in-clinic assessments. Here we introduce the JTrack platform as a secure, reliable and extendable open-source solution for remote monitoring in daily-life and digital phenotyping. Method: JTrack consists of an Android-based smartphone application and a web-based project management dashboard. A wide range of anonymized measurements from motion-sensors, social and physical activities and geolocation information can be collected in either active or passive modes. The dashboard also provides management tools to monitor and manage data collection across studies. To facilitate scaling, reproducibility, data management and sharing we integrated DataLad as a data management infrastructure. JTrack was developed to comply with security, privacy and the General Data Protection Regulation (GDPR) requirements. Results: JTrack is an open-source (released under open-source Apache 2.0 licenses) platform for remote assessment of digital biomarkers (DB) in neurological, psychiatric and other indications. The main components of the JTrack platform and examples of data being collected using JTrack are presented here. Conclusion: Smartphone-based Digital Biomarker data may provide valuable insight into daily life behaviour in health and disease. JTrack provides an easy and reliable open-source solution for collection of such data.

cs.CY↗

arXiv2018

Search-based optimal motion planning for automated driving

This paper presents a framework for fast and robust motion planning designed to facilitate automated driving. The framework allows for real-time computation even for horizons of several hundred meters and thus enabling automated driving in urban conditions. This is achieved through several features. Firstly, a convenient geometrical representation of both the search space and driving constraints enables the use of classical path planning approach. Thus, a wide variety of constraints can be tackled simultaneously (other vehicles, traffic lights, etc.). Secondly, an exact cost-to-go map, obtained by solving a relaxed problem, is then used by A*-based algorithm with model predictive flavour in order to compute the optimal motion trajectory. The algorithm takes into account both distance and time horizons. The approach is validated within a simulation study with realistic traffic scenarios. We demonstrate the capability of the algorithm to devise plans both in fast and slow driving conditions, even when full stop is required.

cs.RO↗

arXiv2018

A novel model-based heuristic for energy optimal motion planning for automated driving

Predictive motion planning is the key to achieve energy-efficient driving, which is one of the main benefits of automated driving. Researchers have been studying the planning of velocity trajectories, a simpler form of motion planning, for over a decade now and many different methods are available. Dynamic programming has shown to be the most common choice due to its numerical background and ability to include nonlinear constraints and models. Although planning of an optimal trajectory is done in a systematic way, dynamic programming does not use any knowledge about the considered problem to guide the exploration and therefore explores all possible trajectories. A* is a search algorithm which enables using knowledge about the problem to guide the exploration to the most promising solutions first. Knowledge has to be represented in a form of a heuristic function, which gives an optimistic estimate of cost for transitioning to the final state, which is not a straightforward task. This paper presents a novel heuristics incorporating air drag and auxiliary power as well as operational costs of the vehicle, besides kinetic and potential energy and rolling resistance known in the literature. Furthermore, optimal cruising velocity, which depends on vehicle aerodynamic properties and auxiliary power, is derived. Results are compared for different variants of heuristic functions and dynamic programming as well.

math.OC↗

arXiv2017

Fluctuations of Wigner-type random matrices associated with symmetric spaces of class DIII and CI

Wigner-type randomizations of the tangent spaces of classical symmetric spaces can be thought of as ordinary Wigner matrices on which additional symmetries have been imposed. In particular, they fall within the scope of a framework, due to Schenker and Schulz-Baldes, for the study of fluctuations of Wigner matrices with additional dependencies among their entries. In this contribution, we complement the results of these authors in that we develop a calculus of patterns which makes it possible to control the asymptotic contributions of dihedral non-crossing pair partitions for the Cartan classes DIII and CI, thus obtaining explicit CLTs for these cases.

math-ph↗

arXiv2013

Lyapunov spectra for all symmetry classes of quasi-one-dimensional disordered systems of non-interacting Fermions

A random phase property is proposed for products of random matrices drawn from any one of the classical groups associated with the ten Cartan symmetry classes of non-interacting disordered Fermion systems. It allows to calculate the Lyapunov spectrum explicitly in a perturbative regime. These results apply to quasi-one-dimensional random Dirac operators which can be constructed as representatives for each of the ten symmetry classes. For those symmetry classes that correspond to two-dimensional topological insulators or superconductors, the random Dirac operators describing the one-dimensional boundaries have vanishing Lyapunov exponents and almost surely an absolutely continuous spectrum, reflecting the gapless and conducting nature of the boundary degrees of freedom.

math-ph↗

arXiv2012

A quantitative central limit theorem for linear statistics of random matrix eigenvalues

It is known that the fluctuations of suitable linear statistics of Haar distributed elements of the compact classical groups satisfy a central limit theorem. We show that if the corresponding test functions are sufficiently smooth, a rate of convergence of order almost $1/n$ can be obtained using a quantitative multivariate CLT for traces of powers that was recently proven using Stein's method of exchangeable pairs.

math.PR↗

arXiv2012

Gaussian Fluctuations for Sample Covariance Matrices with Dependent Data

It is known (Hofmann-Credner and Stolz (2008)) that the convergence of the mean empirical spectral distribution of a sample covariance matrix W_n = 1/n Y_n Y_n^t to the Marčenko-Pastur law remains unaffected if the rows and columns of Y_n exhibit some dependence, where only the growth of the number of dependent entries, but not the joint distribution of dependent entries needs to be controlled. In this paper we show that the well-known CLT for traces of powers of W_n also extends to the dependent case.

math.PR↗

arXiv2011

Stein's method and the multivariate CLT for traces of powers on the classical compact groups

Let $M_n$ be a random element of the unitary, special orthogonal, or unitary symplectic groups, distributed according to Haar measure. By a classical result of Diaconis and Shahshahani, for large matrix size $n$, the vector $ (\on{Tr}(M_n), \on{Tr}(M_n^2),..., \on{Tr}(M_n^d))$ tends to a vector of independent (real or complex) Gaussian random variables. Recently, Jason Fulman has demonstrated that for a single power $j$ (which may grow with $n$), a speed of convergence result may be obtained via Stein's method of exchangeable pairs. In this note, we extend Fulman's result to the multivariate central limit theorem for the full vector of traces of powers.

math.PR↗

arXiv2011

Large deviations for disordered bosons and multiple orthogonal polynomial ensembles

We prove a large deviations principle for the empirical measures of a class of biorthogonal and multiple orthogonal polynomial ensembles that includes biorthogonal Laguerre, Jacobi and Hermite ensembles, the matrix model of Lueck, Sommers and Zirnbauer for disordered bosons, the Stieltjes-Wigert matrix model of Chern-Simons theory, and Angelesco ensembles.

math-ph↗

arXiv2009

A duality approach to the worst case value at risk for a sum of dependent random variables with known covariances

We propose an approach to the aggregation of risks which is based on estimation of simple quantities (such as covariances) associated to a vector of dependent random variables, and which avoids the use of parametric families of copulae. Our main result demonstrates that the method leads to bounds on the worst case Value at Risk for a sum of dependent random variables. Its proof applies duality theory for infinite dimensional linear programs.

q-fin.RM↗

arXiv2008

Borel theorems for random matrices from the classical compact symmetric spaces

We study random vectors of the form $(\operatorname {Tr}(A^{(1)}V),...,\operatorname {Tr}(A^{(r)}V))$, where $V$ is a uniformly distributed element of a matrix version of a classical compact symmetric space, and the $A^{(ν)}$ are deterministic parameter matrices. We show that for increasing matrix sizes these random vectors converge to a joint Gaussian limit, and compute its covariances. This generalizes previous work of Diaconis et al. for Haar distributed matrices from the classical compact groups. The proof uses integration formulas, due to Collins and Śniady, for polynomial functions on the classical compact groups.

math.PR↗

arXiv2008

Asymptotics of matrix integrals and tensor invariants of compact Lie groups

In this paper we give an asymptotic formula for a matrix integral which plays a crucial role in the approach of Diaconis et al. to random matrix eigenvalues. The choice of parameter for the asymptotic analysis is motivated by an invariant theoretic interpretation of this type of integral. For arbitrary regular irreducible representations of arbitrary connected semisimple compact Lie groups, we obtain an asymptotic formula for the trace of certain operators on the space of tensor invariants, thus extending a result of Biane on the dimension of these spaces.

math.RT↗

arXiv2007

Large deviations for random matrix ensembles in mesoscopic physics

In his seminal 1962 paper on the ``threefold way'', Freeman Dyson classified the spaces of matrices that support the random matrix ensembles deemed relevant from the point of view of classical quantum mechanics. Recently, Heinzner, Huckleberry and Zirnbauer have obtained a similar classification based on less restrictive assumptions, thus taking care of the needs of modern mesoscopic physics. Their list is in one-to-one correspondence with the infinite families of Riemannian symmetric spaces as classified by Cartan. The present paper develops the corresponding random matrix theories, with a special emphasis on large deviation principles.

math.PR↗

arXiv2007

Wigner theorems for random matrices with dependent entries: Ensembles associated to symmetric spaces and sample covariance matrices

It is a classical result of Wigner that for an hermitian matrix with independent entries on and above the diagonal, the mean empirical eigenvalue distribution converges weakly to the semicircle law as matrix size tends to infinity. In this paper, we prove analogs of Wigner's theorem for random matrices taken from all infinitesimal versions of classical symmetric spaces. This is a class of models which contains those studied by Wigner and Dyson, along with seven others arising in condensed matter physics. Like Wigner's, our results are universal in that they only depend on certain assumptions about the moments of the matrix entries, but not on the specifics of their distributions. What is more, we allow for a certain amount of dependence among the matrix entries, in the spirit of a recent generalization of Wigner's theorem, due to Schenker and Schulz-Baldes. As a byproduct, we obtain a universality result for sample covariance matrices with dependent entries.

math.PR↗