arXiv subjects

Philipp Schmitz

Publications and source records attributed to Philipp Schmitz.

At least 19 recordsLinked to original sources

arXiv2026

A Continuous-Time Generalization of the LPV Fundamental Lemma

Controller design for physical systems directly from data is of tremendous interest in both the industry and academia. However, the research on direct data-driven control has thus far mainly focused on discrete-time linear time-invariant systems. To make the highly non-trivial step to continuous-time nonlinear systems, this paper explores an intermediate route through the framework of linear parameter-varying (LPV) systems. LPV systems can be used as a convenient surrogate for nonlinear systems to achieve systematic analysis and controller design. In this work, we generalize the LPV Fundamental Lemma for discrete-time systems towards a class of continuous-time LPV systems, achieving data-driven representations that can be used to design continuous-time LPV controllers.

eess.SY↗

arXiv2026

Data-driven feedback rectification of switched linear systems

In this paper, a data-driven method for the computation of stabilizing state-feedbacks is proposed that leads to a rectified eigenstructure of switched linear systems. This means that all switching subsystems have the same sets of eigenvectors and the rectification allows to compute a common quadratic Lyapunov function ensuring asymptotic stability of the closed-loop system. The method is illustrated for two examples including a model of an aerosonde.

math.OC↗

arXiv2026

A data-based image representation for continuous-time LTI systems

We derive a numerically stable method to compute an image representation of an unknown linear system only from data, leveraging a continuous-time version of Willems et al.'s fundamental lemma. To this end, we use derivatives approximated by algebraic differentiators. Our novel image representation avoids solving differential-algebraic equations and significantly reduces computational complexity by eliminating redundant degrees of freedom corresponding to the number of unknown quantities to be identified. Simulation results confirm the effectiveness of the proposed approach, even in the presence of severe measurement disturbances.

math.OC↗

arXiv2025

Excitation of control-affine systems and Koopman error bounds

The Koopman operator and extended dynamic mode decomposition (EDMD) as a data-driven technique for its approximation have attracted considerable attention as a key tool for modeling, analysis, and control of complex dynamical systems. However, extensions towards control-affine systems resulting in bilinear surrogate models are prone to demanding data requirements rendering their applicability intricate. In this paper, we propose a framework for data-fitting of control-affine mappings to increase the robustness margin in the associated system identification problem and, thus, to provide reliable bilinear EDMD schemes. In particular, guidelines for input selection based on subspace angles are deduced such that a desired threshold with respect to the minimal singular value is ensured. Moreover, we derive necessary and sufficient conditions of optimality for maximizing the minimal singular value. Further, we demonstrate the usefulness of the proposed approach using bilinear EDMD with control for nonholonomic robots.

eess.SY↗

arXiv2025

Okapi: Efficiently Safeguarding Speculative Data Accesses in Sandboxed Environments

This paper introduces Okapi, a new hardware/software cross-layer architecture designed to mitigate Transient Execution Side Channel attacks, including Spectre variants, in modern computing systems. Okapi provides a hardware basis for secure speculation in sandboxed environments and can replace expensive speculation barriers in software. At its core, it allows for speculative data accesses to a memory page only after the page has been accessed non-speculatively by the current trust domain. The granularity of the trust domains can be controlled in software to achieve different security and performance trade-offs. For environments with less stringent security needs, the features can be deactivated to remove all performance overhead. Without relying on any software modification, the Okapi hardware features provide full protection against TES breakout attacks, e.g., by Spectre-PHT or Spectre-BTB, at a thread-level granularity. This incurs an average performance overhead of only 3.17% for the SPEC CPU2017 benchmark suite. Okapi introduces the OkapiReset instruction for additional software-level security support. This instruction allows for fine-grained sandboxing with any custom size, resulting in 2.34% performance overhead in our WebAssembly runtime experiment. On top, Okapi provides the possibility to eliminate poisoning attacks. For the highest level of security, the OkapiLoad instruction prevents confidential data from being added to the trust domain after a sequential access, thereby enforcing weak speculative non-interference. In addition, we present a hardware extension that limits the exploitable code space for Spectre gadgets to well-defined sections of the program. Therefore, by ensuring the absence of gadgets in these sections, developers can tailor their software towards achieving beneficial trade-offs between the size of a trust domain and performance.

cs.CR↗

arXiv2025

Sampled-data funnel control and its use for safe continual learning

We propose a novel sampled-data output-feedback controller for nonlinear systems of arbitrary relative degree that ensures reference tracking within prescribed error bounds. We provide explicit bounds on the maximum input signal and the required uniform sampling time. A key strength of this approach is its capability to serve as a safety filter for various learning-based controller designs, enabling the use of learning techniques in safety-critical applications. We illustrate its versatility by integrating it with two different controllers: a reinforcement learning controller and a non-parametric predictive controller based on Willems et al.'s fundamental lemma. Numerical simulations illustrate effectiveness of the combined controller design.

math.OC↗

arXiv2025

Towards Data-Driven Multi-Stage OPF

The operation of large-scale power systems is usually scheduled ahead via numerical optimization. However, this requires models of grid topology, line parameters, and bus specifications. Classic approaches first identify the network topology, i.e., the graph of interconnections and the associated impedances. The power generation schedules are then computed by solving a multi-stage optimal power flow (OPF) problem built around the model. In this paper, we explore the prospect of data-driven approaches to multi-stage optimal power flow. Specifically, we leverage recent findings from systems and control to bypass the identification step and to construct the optimization problem directly from data. We illustrate the performance of our method on a 118-bus system and compare it with the classical identification-based approach.

eess.SY↗

arXiv2024

VeriCHERI: Exhaustive Formal Security Verification of CHERI at the RTL

Protecting data in memory from attackers continues to be a concern in computing systems. CHERI is a promising approach to achieve such protection, by providing and enforcing fine-grained memory protection directly in the hardware. Creating trust for the entire system stack, however, requires a gap-free verification of CHERI's hardware-based protection mechanisms. Existing verification methods for CHERI target the abstract ISA model rather than the underlying hardware implementation. Fully ensuring the CHERI security guarantees for a concrete RTL implementation is a challenge in previous flows and demands high manual efforts. This paper presents VeriCHERI, a novel approach to security verification. It is conceptionally different from previous works in that it does not require any ISA specification. Instead of checking compliance with a golden ISA model, we check against well-established global security objectives of confidentiality and integrity. Fully covering these objectives, VeriCHERI uses as few as four unbounded properties to exhaustively prove or disprove any vulnerability. We demonstrate the effectiveness and scalability of VeriCHERI on a RISC-V based processor implementing a CHERI variant.

cs.CR↗

arXiv2024

A continuous-time fundamental lemma and its application in data-driven optimal control

Data-driven control of discrete-time and continuous-time systems is of tremendous research interest. In this paper, we explore data-driven optimal control of continuous-time linear systems using input-output data. Based on a density result, we rigorously derive error bounds for finite-order polynomial approximations of elements of the system behavior. To this end, we leverage a link between latent variables and flat outputs of controllable systems. Combined with a continuous-time counterpart of the fundamental lemma by Willems et al., we characterize the suboptimality resulting from polynomial approximations in data-driven linear-quadratic optimal control problems. Finally, we draw upon a numerical example to illustrate our results.

math.OC↗

arXiv2024

Fast and memory-efficient optimization for large-scale data-driven predictive control

Recently, data-enabled predictive control (DeePC) schemes based on Willems' fundamental lemma have attracted considerable attention. At the core are computations using Hankel-like matrices and their connection to the concept of persistency of excitation. We propose an iterative solver for the underlying data-driven optimal control problems resulting from linear discrete-time systems. To this end, we apply factorizations based on the discrete Fourier transform of the Hankel-like matrices, which enable fast and memory-efficient computations. To take advantage of this factorization in an optimal control solver and to reduce the effect of inherent bad conditioning of the Hankel-like matrices, we propose an augmented Lagrangian lBFGS-method. We illustrate the performance of our method by means of a numerical study.

math.OC↗

arXiv2023

Safe data-driven reference tracking with prescribed performance

We study output reference tracking for unknown continuous-time systems with arbitrary relative degree. The control objective is to keep the tracking error within predefined time-varying bounds while measurement data is only available at discrete sampling times. To achieve the control objective, we propose a two-component controller. One part is a recently developed sampled-data zero-order hold controller, which achieves reference tracking within prescribed error bounds. To further improve the control signal, we explore the system dynamics via input-output data, and include as the second component a data-driven MPC scheme based on Willems et al.'s fundamental lemma. This combination yields significantly improved input signals as illustrated by a numerical example.

math.OC↗

arXiv2023

Perturbation and spectral theory for singular indefinite Sturm-Liouville operators

We study singular Sturm-Liouville operators of the form \[ \frac{1}{r_j}\left(-\frac{\mathrm d}{\mathrm dx}p_j\frac{\mathrm d}{\mathrm dx}+q_j\right),\qquad j=0,1, \] in $L^2((a,b);r_j)$, where, in contrast to the usual assumptions, the weight functions $r_j$ have different signs near the singular endpoints $a$ and $b$. In this situation the associated maximal operators become self-adjoint with respect to indefinite inner products and their spectral properties differ essentially from the Hilbert space situation. We investigate the essential spectra and accumulation properties of nonreal and real discrete eigenvalues; we emphasize that here also perturbations of the indefinite weights $r_j$ are allowed. Special attention is paid to Kneser type results in the indefinite setting and to $L^1$ perturbations of periodic operators.

math.SP↗

arXiv2023

Behavioral Theory for Stochastic Systems? A Data-driven Journey from Willems to Wiener and Back Again

The fundamental lemma by Jan C. Willems and co-workers, which is deeply rooted in behavioral systems theory, has become one of the supporting pillars of the recent progress on data-driven control and system analysis. This tutorial-style paper combines recent insights into stochastic and descriptor-system formulations of the lemma to further extend and broaden the formal basis for behavioral theory of stochastic linear systems. We show that series expansions -- in particular Polynomial Chaos Expansions (PCE) of $L^2$-random variables, which date back to Norbert Wiener's seminal work -- enable equivalent behavioral characterizations of linear stochastic systems. Specifically, we prove that under mild assumptions the behavior of the dynamics of the $L^2$-random variables is equivalent to the behavior of the dynamics of the series expansion coefficients and that it entails the behavior composed of sampled realization trajectories. We also illustrate the short-comings of the behavior associated to the time-evolution of the statistical moments. The paper culminates in the formulation of the stochastic fundamental lemma for linear (descriptor) systems, which in turn enables numerically tractable formulations of data-driven stochastic optimal control combining Hankel matrices in realization data (i.e. in measurements) with PCE concepts.

math.OC↗

arXiv2022

Lower bounds for self-adjoint Sturm-Liouville operators

In this note we provide estimates for the lower bound of the self-adjoint operator associated with the three-coefficient Sturm-Liouville differential expression $$ \frac{1}{r} \left(-\frac{\mathrm d}{\mathrm dx} p \frac{\mathrm d}{\mathrm dx} + q\right) $$ in the weighted $L^2$-Hilbert space $L^2(\mathbb R; rdx)$.

math.SP↗

arXiv2022

Relative oscillation theory and essential spectra of Sturm--Liouville operators

We develop relative oscillation theory for general Sturm-Liouville differential expressions of the form \[ \frac{1}{r}\left(-\frac{\mathrm d}{\mathrm dx} p \frac{\mathrm d}{\mathrm dx} + q\right) \] and prove perturbation results and invariance of essential spectra in terms of the real coefficients $p$, $q$, $r$. The novelty here is that we also allow perturbations of the weight function $r$ in which case the unperturbed and the perturbed operator act in different Hilbert spaces.

math.SP↗

arXiv2022

Data-driven MPC of descriptor systems: A case study for power networks

Recently, data-driven predictive control of linear systems has received wide-spread research attention. It hinges on the fundamental lemma by Willems et al. In a previous paper, we have shown how this framework can be applied to predictive control of linear time-invariant descriptor systems. In the present paper, we present a case study wherein we apply data-driven predictive control to a discrete-time descriptor model obtained by discretization of the power-swing equations for a nine-bus system. Our results shows the efficacy of the proposed control scheme and they underpin the prospect of the data-driven framework for control of descriptor systems.

eess.SY↗

arXiv2022

Willems' fundamental lemma for linear descriptor systems and its use for data-driven output-feedback MPC

In this paper we investigate data-driven predictive control of discrete-time linear descriptor systems. Specifically, we give a tailored variant of Willems' fundamental lemma, which shows that for descriptor systems the non-parametric modelling via a Hankel matrix requires less data compared to linear time-invariant systems without algebraic constraints. Moreover, we use this description to propose a data-driven framework for optimal control and predictive control of discrete-time linear descriptor systems. For the latter, we provide a sufficient stability condition for receding-horizon control before we illustrate our findings with an example.

math.OC↗

arXiv2021

Perturbations of periodic Sturm--Liouville operators

We study perturbations of the self-adjoint periodic Sturm--Liouville operator \[ A_0 = \frac{1}{r_0}\left(-\frac{\mathrm d}{\mathrm dx} p_0 \frac{\mathrm d}{\mathrm dx} + q_0\right) \] and conclude under $L^1$-assumptions on the differences of the coefficients that the essential spectrum and absolutely continuous spectrum remain the same. If a finite first moment condition holds for the differences of the coefficients, then at most finitely many eigenvalues appear in the spectral gaps. This observation extends a seminal result by Rofe-Beketov from the 1960s. Finally, imposing a second moment condition we show that the band edges are no eigenvalues of the perturbed operator.

math.SP↗