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Philippe Martin

Publications and source records attributed to Philippe Martin.

At least 19 recordsLinked to original sources
arXiv2026

Path-independent Flow Matching for Multi-parameter Generative Dynamics

Flow Matching is a powerful framework for learning transport maps between probability distributions. Yet its standard single-parameter formulation is not designed to capture multi-parameter variations where the resulting transport should be path-independent. Path independence is crucial because it ensures that transformations depend only on the initial and target distributions, not on the specific path. In this work, we introduce Path-independent Flow Matching (PiFM), a method for learning vector fields whose induced flows yield path-independent transport between distributions. We show that PiFM generalizes Flow Matching to higher-dimensional parameter domains while enforcing structural conditions that ensure consistency of composed transformations. In addition, we show that, under suitable assumptions, PiFM approximates the Wasserstein barycenter, linking the framework to a notion of distributional interpolation. To enable practical training, we propose a tractable, simulation-free objective that regresses onto multi-parameter conditional probability paths. We showcase empirically that PiFM outperforms other approaches on both synthetic and real world data in interpolating path-independent trajectories and generating desired out of distribution samples.

cs.LG↗
arXiv2020

Error estimates in Second-order Continuous-Time Sigma-Delta modulators

Continuous-time Sigma-Delta (CT-$\Sigma\Delta$) modulators are oversampling Analog-to-Digital converters that may provide higher sampling rates and lower power consumption than their discrete counterpart. Whereas approximation errors are established for high-order discrete time $\Sigma\Delta$ modulators, theoretical analysis of the error between the filtered output and the input remain scarce. This paper presents a general framework to study this error: under regularity assumptions on the input and the filtering kernel, we prove for a second-order CT-$\Sigma\Delta$ that the error estimate may be in $o(1/N^2)$, where $N$ is the oversampling ratio. The whole theory is validated by numerical experiments.

eess.SP↗
arXiv2020

Size Dependence of Lattice Parameter and Electronic Structure in CeO 2 Nanoparticles

Intrinsic properties of a compound (e.g., electronic structure, crystallographic structure, optical and magnetic properties) define notably its chemical and physical behavior. In the case of nanomaterials, these fundamental properties depend on the occurrence of quantum mechanical size effects and on the considerable increase of the surface to bulk ratio. Here, we explore the size dependence of both crystal and electronic properties of CeO2 nanoparticles (NPs) with different sizes by state-of-the art spectroscopic techniques. X-ray diffraction, X-ray photoelectron spectroscopy, and high-energy resolution fluorescence-detection hard X-ray absorption near-edge structure (HERFD-XANES) spectroscopy demonstrate that the as-synthesized NPs crystallize in the fluorite structure and they are predominantly composed of CeIV ions. The strong dependence of the lattice parameter with the NPs size was attributed to the presence of adsorbed species at the NPs surface thanks to Fourier transform infrared spectroscopy and thermogravimetric analysis measurements. In addition, the size dependence of the t2g states in the Ce LIII XANES spectra was experimentally observed by HERFD-XANES and confirmed by theoretical calculations.

physics.chem-ph↗
arXiv2020

Sensorless rotor position estimation by PWM-induced signal injection

We demonstrate how the rotor position of a PWM-controlled PMSM can be recovered from the measured currents, by suitably using the excitation provided by the PWM itself. This provides the benefits of signal injection, in particular the ability to operate even at low velocity, without the drawbacks of an external probing signal. We illustrate the relevance of the approach by simulations and experimental results.

eess.SY↗
arXiv2020

Adding virtual measurements by PWM-induced signal injection

We show that for PWM-operated devices, it is possible to benefit from signal injection \emph{without an external probing signal}, by suitably using the excitation provided by the PWM itself. As in the usual signal injection framework conceptualized in [1], an extra "virtual measurement" can be made available for use in a control law, but without the practical drawbacks caused by an external signal.

math.OC↗
arXiv2018

Exact controllability of a linear Korteweg-de Vries equation by the flatness approach

We consider a linear Korteweg-de Vries equation on a bounded domain with a left Dirichlet boundary control.The controllability to the trajectories of such a system was proved in the last decade by using Carleman estimates.Here, we go a step further by establishing the exact controllability in a space of analytic functions with the aid of the flatness approach.

math.AP↗
arXiv2017

Delay-robust control design for two heterodirectional linear coupled hyperbolic PDEs

We detail in this article the necessity of a change of paradigm for the delay-robust control of systems composed of two linear first order hyperbolic equations. One must go back to the classical trade-off between convergence rate and delay-robustness. More precisely, we prove that, for systems with strong reflections, canceling the reflection at the actuated boundary will yield zero delay-robustness. Indeed, for such systems, using a backstepping-controller, the corresponding target system should preserve a small amount of this reflection to ensure robustness to a small delay in the loop. This implies, in some cases, giving up finite time convergence.

math.OC↗
arXiv2017

Obtaining the Current-Flux Relations of the Saturated PMSM by Signal Injection

This paper proposes a method based on signal injection to obtain the saturated current-flux relations of a PMSM from locked-rotor experiments. With respect to the classical method based on time integration, it has the main advantage of being completely independent of the stator resistance; moreover, it is less sensitive to voltage biases due to the power inverter, as the injected signal may be fairly large.

eess.SY↗
arXiv2017

Controllability of the 1D Schr\"odinger equation using flatness

We derive in a direct way the exact controllability of the 1D free Schr\"odinger equation with Dirichlet boundary control. We use the so-called flatness approach, which consists in parametrizing the solution and the control by the derivatives of a "flat output". This provides an explicit and very regular control achieving the exact controllability in the energy space.

math.OC↗
arXiv2016

Energy-based Modeling of AC Motors

We propose an approach to modeling of AC motors entirely based on analytical mechanics. Symmetry and connection constraints are moreover incorporated in the energy function from which the models are derived. The approach is especially suited to handle magnetic saturation, but also directly recovers the standard unsaturated models of the literature. The theory is illustrated by some experimental data.

math.OC↗
arXiv2016

A global exponential observer for velocity-aided attitude estimation

We propose a simple nonlinear observer for estimating the attitude and velocity of a rigid body from the measurements of specific acceleration, angular velocity, magnetic field (in body axes), and linear velocity (in body axes). It is uniformly globally exponentially convergent, and also enjoys other nice properties: global decoupling of pitch and roll estimation from magnetic measurements, good local behavior, and easy tuning. The observer is "geometry-free", in the sense that it respects only asymptotically the rotational geometry. The good behavior of the observer, even when the measurements are noisy and biased is illustrated in simulation.

math.OC↗
arXiv2016

A global observer for attitude and gyro biases from vector measurements

We consider the classical problem of estimating the attitude and gyro biases of a rigid body from vector measurements and a triaxial rate gyro. We propose a simple "geometry-free" nonlinear observer with guaranteed uniform global asymptotic convergence and local exponential convergence; the stability analysis, which relies on a strict Lyapunov function, is rather simple. The excellent behavior of the observer is illustrated through a detailed numerical simulation.

math.OC↗
arXiv2015

An analysis of the benefits of signal injection for low-speed sensorless control of induction motors

We analyze why low-speed sensorless control of the IM is intrinsically difficult, and what is gained by signal injection. The explanation relies on the control-theoretic concept of observability applied to a general model of the saturated IM. We show that the IM is not observable when the stator speed is zero in the absence of signal injection, but that observability is restored thanks to signal injection and magnetic saturation. The analysis also reveals that existing sensorless algorithms based on signal injection may perform poorly for some IMs under particular operating conditions. The approach is illustrated by simulations and experimental data.

math.OC↗
arXiv2015

A semi-global model-based state estimator for the quadrotor using only inertial measurements

We propose a nonlinear observer to estimate the state (orientation and in-plane velocity vector) of the quadrotor, based on a drag-force-enhanced model. It is an alternative to recent works using a similar model together with an Extended Kalman Filter (EKF). But while enjoying the benefits of an enhanced model, it does not have the usual drawbacks of an EKF: indeed, the computational cost is much lower, the tuning is easier, and above all the guaranteed domain of convergence is very large.

math.OC↗
arXiv2015

Adding virtual measurements by signal injection

We propose a method to "create" a new measurement output by exciting the system with a high-frequency oscillation. This new "virtual" measurement may be useful to facilitate the design of a suitable control law. The approach is especially interesting when the observability from the actual output degenerates at a steady-state regime of interest. The proposed method is based on second-order averaging and is illustrated by simulations on a simple third-order system.

math.OC↗
arXiv2015

On the reachable states for the boundary control of the heat equation

We are interested in the determination of the reachable states for the boundary control of the one-dimensional heat equation. We consider either one or two boundary controls. We show that reachable states associated with square integrable controls can be extended to analytic functions onsome square of C, and conversely, that analytic functions defined on a certain disk can be reached by using boundary controlsthat are Gevrey functions of order 2. The method of proof combines the flatness approach with some new Borel interpolation theorem in some Gevrey class witha specified value of the loss in the uniform estimates of the successive derivatives of the interpolating function.

math.AP↗
arXiv2014

Velocity-aided Attitude Estimation for Accelerated Rigid Bodies

Two nonlinear observers for velocity-aided attitude estimation, relying on gyrometers, accelerometers, magnetometers, and velocity measured in the body-fixed frame, are proposed. As opposed to state-of-the-art body-fixed velocity-aided attitude observers endowed with local properties, both observers are (almost) globally asymptotically stable, with very simple and flexible tuning. Moreover, the roll and pitch estimates are globally decoupled from magnetometer measurements.

math.OC↗