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Philippe Martin

Philippe Martin appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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math.OCmath.APSystems and Controleess.SYHardware ArchitectureMachine Learningphysics.ins-det

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Published work

23 published item(s)

preprint2026arXiv

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.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

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.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

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.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

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.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

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.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

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.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

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.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

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.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Null controllability of one-dimensional parabolic equations by the flatness approach

We consider linear one-dimensional parabolic equations with space dependent coefficients that are only measurable and that may be degenerate or singular.Considering generalized Robin-Neumann boundary conditions at both extremities, we prove the null controllability with one boundary control by following the flatness approach, which providesexplicitly the control and the associated trajectory as series. Both the control and the trajectory have a Gevrey regularity in time related to the $L^p$ class of the coefficient in front of $u\_t$.The approach applies in particular to the (possibly degenerate or singular) heat equation $(a(x)u\_x)\_x-u\_t=0$ with $a(x)\textgreater{}0$ for a.e. $x\in (0,1)$ and $a+1/a \in L^1(0,1)$, or to the heat equation with inverse square potential $u\_{xx}+(μ / |x|^2)u-u\_t=0$with $μ\ge 1/4$.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

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.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Controllability of the 1D Schrodinger equation by the flatness approach

We derive in a straightforward way the exact controllability of the 1-D Schrodinger equation with a Dirichlet boundary control. We use the so-called flatness approach, which consists in parameterizing the solution and the control by the derivatives of a "flat output". This provides an explicit control input achieving the exact controllability in the energy space. As an application, we derive an explicit pair of control inputs achieving the exact steering to zero for a simply-supported beam.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Energy-based modeling of electric motors

We propose a new approach to model electrical machines based on energy considerations and construction symmetries of the motor. We detail the approach on the Permanent-Magnet Synchronous Motor and show that it can be extended to Synchronous Reluctance Motor and Induction Motor. Thanks to this approach we recover the usual models without any tedious computation. We also consider effects due to non-sinusoidal windings or saturation and provide experimental data.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

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.

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

Null controllability of the 1D heat equation using flatness

We derive in a straightforward way the null controllability of a 1-D heat equation with boundary control. We use the so-called {\em flatness approach}, which consists in parameterizing the solution and the control by the derivatives of a "flat output". This provides an explicit control law achieving the exact steering to zero. We also give accurate error estimates when the various series involved are replaced by their partial sums, which is paramount for an actual numerical scheme. Numerical experiments demonstrate the relevance of the approach.

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

Null Controllability of the 2D Heat Equation Using Flatness

We derive in a direct and rather straightforward way the null controllability of a 2-D heat equation with boundary control. We use the so-called flatness approach, which consists in parameterizing the solution and the control by the derivatives of a "flat output". This provides an explicit control law achieving the exact steering to zero. Numerical experiments demonstrate the relevance of the approach.

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

Null controllability of the heat equation using flatness

We derive in a direct and rather straightforward way the null controllability of the N-dimensional heat equation in a bounded cylinder with boundary control at one end of the cylinder. We use the so-called flatness approach, which consists in parameterizing the solution and the control by the derivatives of a "flat output". This yields an explicit control law achieving the exact steering to zero. Replacing the involved series by partial sums we obtain a simple numerical scheme for which we give explicit error bounds. Numerical experiments demonstrate the relevance of the approach.

0 citations0 reviewsNo code linkedOpen access
preprint2012arXiv

Sensorless position estimation of Permanent-Magnet Synchronous Motors using a saturation model

Sensorless control of Permanent-Magnet Synchronous Motors (PMSM) at low velocity remains a challenging task. A now well-established method consists in injecting a high-frequency signal and use the rotor saliency, both geometric and magnetic-saturation induced. This paper proposes a clear and original analysis based on second-order averaging of how to recover the position information from signal injection; this analysis blends well with a general model of magnetic saturation. It also proposes a simple parametric model of the saturated PMSM, based on an energy function which simply encompasses saturation and cross-saturation effects. Experimental results on a surface-mounted PMSM and an interior magnet PMSM illustrate the relevance of the approach.

0 citations0 reviewsNo code linkedOpen access
preprint2012arXiv

Signal injection and averaging for position estimation of Permanent-Magnet Synchronous Motors

Sensorless control of Permanent-Magnet Synchronous Motors at low velocity remains a challenging task. A now well-established method consists in injecting a high-frequency signal and use the rotor saliency, both geometric and magnetic-saturation induced. This paper proposes a clear and original analysis based on second-order averaging of how to recover the position information from signal injection; this analysis blends well with a general model of magnetic saturation. It also experimentally demonstrates the relevance for position estimation of a simple parametric saturation model recently introduced by the authors.

0 citations0 reviewsNo code linkedOpen access
preprint2011arXiv

Estimation of Saturation of Permanent-Magnet Synchronous Motors Through an Energy-Based Model

We propose a parametric model of the saturated Permanent-Magnet Synchronous Motor (PMSM) together with an estimation method of the magnetic parameters. The model is based on an energy function which simply encompasses the saturation effects. Injection of fast-varying pulsating voltages and measurements of the resulting current ripples then permit to identify the magnetic parameters by linear least squares. Experimental results on a surface-mounted PMSM and an interoir magnet PMSM illustrate the relevance of the approach.

0 citations0 reviewsNo code linkedOpen access
preprint2011arXiv

Null controllability of the structurally damped wave equation with moving point control

We investigate the internal controllability of the wave equation with structural damping on the one dimensional torus. We assume that the control is acting on a moving point or on a moving small interval with a constant velocity. We prove that the null controllability holds in some suitable Sobolev space and after a fixed positive time independent of the initial conditions.

0 citations0 reviewsNo code linkedOpen access
preprint2010arXiv

A Separation Principle on Lie Groups

For linear time-invariant systems, a separation principle holds: stable observer and stable state feedback can be designed for the time-invariant system, and the combined observer and feedback will be stable. For non-linear systems, a local separation principle holds around steady-states, as the linearized system is time-invariant. This paper addresses the issue of a non-linear separation principle on Lie groups. For invariant systems on Lie groups, we prove there exists a large set of (time-varying) trajectories around which the linearized observer-controler system is time-invariant, as soon as a symmetry-preserving observer is used. Thus a separation principle holds around those trajectories. The theory is illustrated by a mobile robot example, and the developed ideas are then extended to a class of Lagrangian mechanical systems on Lie groups described by Euler-Poincare equations.

0 citations0 reviewsNo code linkedOpen access
preprint2007arXiv

Design of a Virtual Component Neutral Network-on-Chip Transaction Layer

Research studies have demonstrated the feasibility and advantages of Network-on-Chip (NoC) over traditional bus-based architectures but have not focused on compatibility communication standards. This paper describes a number of issues faced when designing a VC-neutral NoC, i.e. compatible with standards such as AHB 2.0, AXI, VCI, OCP, and various other proprietary protocols, and how a layered approach to communication helps solve these issues.

0 citations0 reviewsNo code linkedOpen access