arXiv subjects

Charles Poussot-Vassal

Publications and source records attributed to Charles Poussot-Vassal.

At least 19 recordsLinked to original sources

arXiv2026

Rational approximation for Zolotarev sign and ratio problems

We study algorithms for Zolotarev (3rd and 4th) problems rational approximation. First, we show that the Loewner framework (LF) is appropriate to rapidly and with no iterations, approximate the Zolotarev problems by compressing the (numerous) interpolation conditions. Second, we compare the approximation properties (e.g. coefficients and poles) of LF with the standard AAA, AAA-sign and its AAA-Lawson variants. We concentrate the study on a canonical example, namely the symmetric two-circles one, for which the optimal solution is well documented. For this case, we highlight the numerical robustness of LF and its ability to recover the structure of the optimal solution. Additional non-trivial geometries are also reported, emphasizing that LF is fast, reliable, and yields accurate approximants with no user intervention.

math.NA↗

arXiv2026

Non-intrusive nonlinear reduced-order modeling with variable projection

This work presents a method for constructing nonlinear reduced-order models from input-output time-domain data. The proposed approach, termed Mixed Interpolatory Inference with Variable Projection (MIIvp), exploits the fact that the considered class of nonlinear state-space models is linear in the output equation parameters. By applying the Variable Projection (VarPro) algorithm, the optimization is restricted to the state equation parameters alone, while the output equation parameters are recovered via linear least squares. As a consequence, the output dimension does not enter the nonlinear optimization parameter vector, making the method well suited for systems with very high-dimensional outputs, a setting where many other approaches become computationally prohibitive. Under mild assumptions, it is shown that MIIvp can recover the true model parameters up to similarity. The method is first validated on a synthetic bilinear system, where it achieves machine-precision accuracy and recovers the true eigenvalues. MIIvp is then compared with existing methods on two experimental benchmarks from the nonlinear system identification literature. These numerical experiments showcase both the validity and the limitations of the proposed approach. Finally, directions for improvements and future work are outlined.

eess.SY↗

arXiv2026

Tensor-based multivariate function approximation: methods benchmarking and comparison

We evaluate some methods designed for tensor- (or data-) based multivariate model construction (approximation and compression). To this aim, a collection of multivariate functions and an evaluation methodology are suggested. First, these functions, with varying complexity (e.g., number and degree of the variables) and nature (e.g., rational, irrational, differentiable or not, symmetric, etc.) are used to build $n$-dimensional tensors, each of different dimension and memory size. Second, grounded on this tensor, we evaluate the performances of different methods and implementations leading to different types of surrogate models (e.g., rational functions, networks). The accuracy, the computational time, the parameter tuning impact, etc. are monitored and reported. One objective is to evaluate the different available strategies to guide users on the prospects, advantages, and limits of the various tools. The contributions are twofold: (i) to suggest a comprehensive benchmark collection together with a methodology for tensor approximation with a surrogate model and, in addition, (ii) to provide a digest and additional details of the multivariate Loewner Framework (mLF) approach [Antoulas et al., 2025], as well as detailed examples and code.

math.NA↗

arXiv2025

On the Loewner framework, the Kolmogorov superposition theorem, and the curse of dimensionality

The Loewner framework is an interpolatory approach for the approximation of linear and nonlinear systems. The purpose here is to extend this framework to linear parametric systems with an arbitrary number n of parameters. To achieve this, a new generalized multivariate rational function realization is proposed. Then, we introduce the n-dimensional multivariate Loewner matrices and show that they can be computed by solving a set of coupled Sylvester equations. The null space of these Loewner matrices allows the construction of the multivariate barycentric rational function. The principal result of this work is to show how the null space of the n-dimensional Loewner matrix can be computed using a sequence of 1-dimensional Loewner matrices, leading to a drastic reduction of the computational burden. Equally importantly, this burden is alleviated by avoiding the explicit construction of large-scale n-dimensional Loewner matrices of size $N \times N$. Instead, the proposed methodology achieves decoupling of variables, leading to (i) a complexity reduction from $O(N^3)$ to below $O(N^{1.5})$ when $n > 5$ and (ii) to memory storage bounded by the largest variable dimension rather than their product, thus taming the curse of dimensionality and making the solution scalable to very large data sets. This decoupling of the variables leads to a result similar to the Kolmogorov superposition theorem for rational functions. Thus, making use of barycentric representations, every multivariate rational function can be computed using the composition and superposition of single-variable functions. Finally, we suggest two algorithms (one direct and one iterative) to construct, directly from data, multivariate (or parametric) realizations ensuring (approximate) interpolation. Numerical examples highlight the effectiveness and scalability of the method.

math.NA↗

arXiv2024

Structure-Preserving Discretization and Model Order Reduction of Boundary-Controlled 1D Port-Hamiltonian Systems

This paper presents a systematic methodology for the discretization and reduction of a class of one-dimensional Partial Differential Equations (PDEs) with inputs and outputs collocated at the spatial boundaries. The class of system that we consider is known as Boundary-Controlled Port-Hamiltonian Systems (BC-PHSs) and covers a wide class of Hyperbolic PDEs with a large type of boundary inputs and outputs. This is, for instance, the case of waves and beams with Neumann, Dirichlet, or mixed boundary conditions. Based on a Partitioned Finite Element Method (PFEM), we develop a numerical scheme for the structure-preserving spatial discretization for the class of one-dimensional BC-PHSs. We show that if the initial PDE is passive (or impedance energy preserving), the discretized model also is. In addition and since the discretized model or Full Order Model (FOM) can be of large dimension, we recall the standard Loewner framework for the Model Order Reduction (MOR) using frequency domain interpolation. We recall the main steps to produce a Reduced Order Model (ROM) that approaches the FOM in a given range of frequencies. We summarize the steps to follow in order to obtain a ROM that preserves the passive structure as well. Finally, we provide a constructive way to build a projector that allows to recover the physical meaning of the state variables from the ROM to the FOM. We use the one-dimensional wave equation and the Timoshenko beam as examples to show the versatility of the proposed approach.

math.NA↗

arXiv2024

Scattering-Passive Structure-Preserving Finite Element Method for the Boundary Controlled Transport Equation with a Moving Mesh

A structure-preserving Finite Element Method (FEM) for the transport equation in one- and two-dimensional domains is presented. This Distributed Parameter System (DPS) has non-collocated boundary control and observation, and reveals a scattering-energy preserving structure. We show that the discretized model preserves the aforementioned structure from the original infinite-dimensional system. Moreover, we analyse the case of moving meshes for the one-dimensional case. The moving mesh requires less states than the fixed one to produce solutions with a comparable accuracy, and it can also reduce the overshoot and oscillations of Gibbs phenomenon produced when using the FEM. Numerical simulations are provided for the case of a one-dimensional transport equation with fixed and moving meshes.

math.NA↗

arXiv2023

Data-driven port-Hamiltonian structured identification for non-strictly passive systems

In this work, we detail a procedure to construct a reduced order model on the basis of frequency-domain data, that preserves the non-strictly passive property and the port-Hamiltonian structure. The proposed scheme is based on Benner et al. (2020) contribution, which has been adapted (i) to handle non-strictly passive model, and (ii) to handle numerical issues observed when applying the Loewner framework on complex configurations. We validate the proposed scheme on a very complex two-dimensional wave equation, for which the discretized version preserves the port-Hamiltoninan form.

eess.SY↗

arXiv2021

Constructive interpolation points selection in the Loewner framework

This note describes a constructive heuristic to select frequencies of interest within the context of reduced-order modelling by interpolation. The approach is described here through the Loewner framework. Numerical illustrations highlight the benefit it can bring to decrease the required number of interpolation points which is key when the data come from numerically expensive solvers.

math.NA↗

arXiv2021

Data-driven modeling and control of large-scale dynamical systems in the Loewner framework

In this contribution, we discuss the modeling and model reduction framework known as the Loewner framework. This is a data-driven approach, applicable to large-scale systems, which was originally developed for applications to linear time-invariant systems. In recent years, this method has been extended to a number of additional more complex scenarios, including linear parametric or nonlinear dynamical systems. We will provide here an overview of the latter two, together with time-domain extensions. Additionally, the application of the Loewner framework is illustrated by a collection of practical test cases. Firstly, for data-driven complexity reduction of the underlying model, and secondly, for dealing with control applications of complex systems (in particular, with feedback controller design).

eess.SY↗

arXiv2021

Performance evaluation of gust load alleviation systems for flexible aircraft via optimal control

The dynamical response of an aircraft subject to gust perturbations is a key element in a preliminary design phase. In particular, the loads induced by gusts along the wing should not exceed some limit values and should even ideally be decreased. Active control is one lever to address this problem. However, evaluating the benefit that active control may bring considering some actuators characteristics or some delay in the loop is a difficult task, especially in the early design phase. This problem is addressed in this paper with an open-loop optimal control framework and more specifically with a direct transcription method resulting in a linear optimisation problem. The approach is illustrated on a realistic aeroelastic aircraft model built with a coupled fluid-structure solver which order is reduced to decrease the number of optimisation variables.

eess.SY↗

arXiv2021

Interpolatory-based data-driven pulsed fluidic actuator control design and experimental validation

Pulsed fluidic actuators play a central role in the fluid flow experimental control strategy to achieve better performances of aeronautic devices. In this paper, we demonstrate, through an experimental test bench, how the interpolatory-based Loewner Data-Driven Control (L-DDC) framework is an appropriate tool for accurately controlling the outflow velocity of this family of actuators. L-DDC combines the concept of ideal controller with the Loewner framework in a single data-driven rationale, appropriate to experimental users. The contributions of the paper are, first, to emphasise the simplicity and versatility of such a data-driven rationale in a constrained experimental setup, and second, to solve some practical fluid engineers concerns by detailing the complete workflow and key ingredients for successfully implementing a pulsed fluidic actuator controller from the data acquisition to the control implementation and validation stages.

physics.flu-dyn↗

arXiv2020

Interpolatory Methods for Generic BizJet Gust Load Alleviation Function

The paper's main contribution concerns the use of interpolatory methods to solve end to end industrial control problems involving complex linear dynamical systems. More in details, contributions show how the rational data and function interpolation framework is a pivotal tool (i) to construct (frequency-limited) reduced order dynamical models appropriate for model-based control design and (ii) to accurately discretise controllers in view of on-board computer-limited implementation. These contributions are illustrated along the paper through the design of an active feedback gust load alleviation function, applied on an industrial generic business jet aircraft use-case. The closed-loop validation and performances evaluation are assessed through the use of an industrial dedicated simulator and considering certification objectives. Although application is centred on aircraft applications, the method is not restrictive and can be extended to any linear dynamical systems.

eess.SY↗

arXiv2020

Mixed interpolatory and inference non-intrusive reduced order modeling with application to pollutants dispersion

On the basis of input-output time-domain data collected from a complex simulator, this paper proposes a constructive methodology to infer a reduced-order linear, bilinear or quadratic time invariant dynamical model reproducing the underlying phenomena. The approach is essentially based on linear dynamical systems and approximation theory. More specifically, it sequentially involves the interpolatory Pencil and Loewner framework, known to be both very versatile and scalable to large-scale data sets, and a linear least square problem involving the raw data and reduced internal variables. With respect to intrusive methods, no prior knowledge on the operator is needed. In addition, compared to the traditional non-intrusive operator inference ones, the proposed approach alleviates the need of measuring the original full-order model internal variables. It is thus applicable to a wider application range than standard intrusive and non-intrusive methods. The rationale is successfully applied on a large eddy simulation of a pollutants dispersion case over an airport area involving multi-scale and multi-physics dynamical phenomena. Despite the simplicity of the resulting low complexity model, the proposed approach shows satisfactory results to predict the pollutants plume pattern while being significantly faster to simulate.

math.DS↗

arXiv2020

Interpolation-based irrational model control design and stability analysis

The versatility of data-driven approximation by interpolatory methods, originally settled for model approximation purpose, is illustrated in the context of linear controller design and stability analysis of irrational models. To this aim, following an academic driving example described by a linear partial differential equation, it is shown how the Loewner-based interpolation may be an essential ingredient for control design and stability analysis. More specifically, the interpolatory framework is first used to approximate the irrational model by a rational one that can be used for model-based control, and secondly, it is used for direct data-driven control design, showing equivalent results. Finally, this interpolation framework is employed for estimating the stability of the interconnection of the irrational model with a rational controller.

math.OC↗

arXiv2020

On Loewner data-driven control for infinite-dimensional systems

In this paper, we address extensions of the Loewner Data-Driven Control (L-DDC) methodology. First, this approach is extended by incorporating two alternative approximation methods known as Adaptive-Antoulas-Anderson (AAA) and Vector Fitting (VF). These algorithms also include least squares fitting which provides additional flexibility and enables possible adjustments for control tuning. Secondly, the standard model reference data-driven setting is extended to handle noise affecting the data and uncertainty in the closed-loop objective function. These proposed adaptations yield a more robust data-driven control design.

math.OC↗

arXiv2020

Optimal Modal Truncation

This paper revisits the modal truncation from an optimisation point of view. In particular, the concept of dominant poles is formulated with respect to different systems norms as the solution of the associated optimal modal truncation problem. The latter is reformulated as an equivalent convex integer or mixed-integer program. Numerical examples highlight the concept and optimisation approach.

math.OC↗

arXiv2020

Yet another introduction to linear dynamical systems control: From identification and approximation to digital control

This report aims at presenting (yet) a(nother) methodology to design and implement a linear controller for linear dynamical systems on practical applications. The specificity of this report is that authors try to cover (obviously in a non exhaustive way) a wide range of control engineering fields. Indeed, the main purpose is to give a quick overview of standard control engineer approaches to non familiar readers. More specifically, using a simple toy example, we discuss the main steps control engineers usually follow. Namely, (i) the excitation signals construction, (ii) the (continuous-time) linear model construction and approximation, (iii) the (continuous-time) control design, and finally, (iv) its time-domain discretisation and control signal modulation in view of practical implementation. This report is clearly user-oriented and thus focuses on practical aspects (using Matlab code) rather than on theoretical ones, let to the reader's curiosity with few but relevant references.

eess.SY↗

arXiv2019

Technical note: Hybrid Loewner Data Driven Control

This note describes how the Loewner framework can be exploited to create a discrete-time control-law from frequency-data of a continuous-time plant so that their hybrid interconnection matches a given continuous-time reference model up to the Nyquist frequency. The resulting Hybrid Loewner Data Driven Control scheme is illustrated on two numerical examples.

eess.SY↗