arXiv subjects

Yann Le Gorrec

Publications and source records attributed to Yann Le Gorrec.

At least 19 recordsLinked to original sources

arXiv2026

The distance-based formation controller design for multi-agent systems in port-Hamiltonian form

Based on the practical scenario where collisions in formation control may lead to agent damage, this paper investigates the integrated problem of distance-based formation control and collision avoidance for multi-agent systems governed by port-Hamiltonian dynamics. A foundational step involves constructing a signed incidence matrix, which, by design, corresponds to a directed acyclic graph and possesses the full column rank property. To overcome the prevalent issue of local minima in traditional artificial potential fields, a novel design utilizing attraction-only potentials is introduced, with collision avoidance rigorously enforced by safety barriers. This framework leads to a unified controller that concurrently manages velocity tracking, target formation acquisition, and inter-agent safety. The stability of the resulting closed-loop system is guaranteed through LaSalle's invariance principle. Numerical simulations demonstrate the validity and effectiveness of the proposed control strategy.

math.OC↗

arXiv2026

Strong imposition of Dirichlet boundary velocities in structure-preserving discretizations of elastodynamics

The imposition of boundary velocities in finite element models of port-Hamiltonian elastodynamics typically relies on Lagrange multipliers, yielding Differential-Algebraic Equations (DAEs). Alternatively, weak imposition methods that maintain an Ordinary Differential Equation (ODE) structure often exhibit poor accuracy at Dirichlet boundaries. To address these limitations, this paper introduces an additive kinematic decomposition at the continuous level, splitting the displacement and velocity fields into a relative dynamic component that vanishes on the boundary and a prescribed lifting function extending into the interior domain. This decomposition induces a distributed port that maps the effects of the boundary actuation inside the domain. By incorporating this mapping into suitable virtual power principles, we derive lifted port-Hamiltonian system (PHS) models that, upon finite element discretization, reduce to ODE systems in which Dirichlet boundary velocities are strongly imposed. The framework is applied to derive 2-field and 4-field formulations suited to distinct PHS geometric representations. Furthermore, we show that under specific shape functions, standard FEM schemes are recovered, demonstrating that the lifting framework in the discrete models is equivalent to the classic algebraic matrix partitioning in computational mechanics practice. The energy-balance properties and computational performance of the proposed methodology are verified through numerical simulations.

cs.CE↗

arXiv2026

Design and Modeling of a HASEL Actuator-Based Micro Parallel Robot

This paper presents the mechatronic design, dynamic modeling, and experimental validation of a three-degree-of-freedom (3-DOF) micro parallel robot featuring a prismatic-spherical (3PS) topology actuated by three Hydraulically Amplified Self-Healing Electrostatic (HASEL) actuators. Each soft actuator provides the prismatic motion of an individual limb, while a compliant interface to the moving platform functions as a spherical joint. A prototype incorporating three base-integrated HASEL actuators was fabricated, and the platform motion was measured using an XY laser-tracking system. For control purposes, a port-Hamiltonian (PH) model, combined with the mechanism's forward kinematics (FKM), is developed to capture the robot's nonlinear dynamic behavior, whereas the inverse kinematics (IKM) is employed to estimate the required actuator displacements. Model parameters were identified using nonlinear grey-box (NLGB) estimation, yielding a compact and control-oriented representation suitable for subsequent controller design.

math.OC↗

arXiv2026

Observer-Based State Feedback Controller for a Mindlin Plate Model in port-Hamiltonian framework

This paper generalises an early lumped observer-based state-feedback (OBSF) control design methodology, originally developed for one-dimensional (1-D) boundary-controlled port-Hamiltonian systems, to a two-dimensional (2-D) boundary-controlled Mindlin plate. To this end, the 2-D port-Hamiltonian Mindlin plate model is first introduced and then discretized using a structure-preserving finite-difference method on staggered grids. A controllability decomposition is subsequently applied to identify the controllable modes of the discretized model. Furthermore, the state-feedback and observer gains are designed so that the OBSF controller is strictly positive real. This guarantees the stability of the closed-loop system when the finite-dimensional OBSF controller is interconnected with the 2-D boundary-controlled Mindlin plate. Numerical simulations are finally presented to illustrate the effectiveness of the proposed method.

math.OC↗

arXiv2026

PH-KAN: Port-Hamiltonian Kolmogorov-Arnold Network

Data-driven machine learning approaches have become increasingly attractive for nonlinear system identification, but standard models often fail to preserve the underlying physical structure and remain difficult to interpret, especially when no analytical model is available. In this context, port-Hamiltonian (pH) models provide a natural physics-informed representation. However, when these models are parameterized with standard multilayer perceptrons (MLPs), the learned constitutive components often remain poorly interpretable. In this paper, we propose a structure-preserving identification framework for nonlinear port-Hamiltonian systems based on Kolmogorov-Arnold Networks (KANs). The proposed PH-KAN model parameterizes the interconnection matrix, dissipation matrix, Hamiltonian, and input mapping using dedicated KAN blocks, while enforcing the port-Hamiltonian constraints by construction. This yields constitutive representations in which the nonlinear functions defining the identified pH components can be explicitly inspected, leading to a more interpretable model than with standard MLP-based parameterizations.

math.OC↗

arXiv2026

Observer design for classes of nonlinear port-Hamiltonian systems

This paper presents a systematic observer design methodology for a class of port-Hamiltonian (pH) systems with state-dependent input matrices. Such systems can model a wide range of electromechanical systems, including magnetic levitation systems, MEMS devices, and electro-active polymer actuators such as DEA actuators, HASEL actuators, etc. In these applications, state-dependent input matrices naturally arise when the system is modeled under quasi-static electrical assumptions. An LPV polytopic embedding framework, together with LMI-based synthesis conditions, is proposed. The nonlinear error dynamics are represented as a convex combination of linear vertex systems using an integral mean value representation, which enables systematic computation of the observer gains that ensures exponential convergence. Both constant-gain and gain-scheduled observers are derived. Numerical results demonstrate the effectiveness of the proposed observer, with the gain-scheduled design achieving a significant increase in the maximum certifiable decay rate compared with constant-gain approaches, thereby reducing conservatism.

math.OC↗

arXiv2026

Privacy-Preserving Formation Control for Networked Underactuated USVs: A Passivity-Based Approach

This paper studies coordinated trajectory planning and tracking control for multiple unmanned surface vessels (USVs) under strict privacy requirements. To avoid the privacy risks associated with direct position sharing in conventional cooperative methods, the proposed approach adopts an estimated fleet centroid as the only shared variable, preventing individual trajectory disclosure while enabling coordination. Based on this interaction mechanism, a formation-oriented trajectory is generated for the fleet. The collective dynamics are modeled using Port-Hamiltonian systems, and a passivity-based tracking controller is designed for each USV to accurately follow the planned trajectories. The stability of the closed-loop system is rigorously proven, and experiments on a real USV platform confirm effective formation tracking and privacy preservation. The proposed result extends and validates through experimental results the approach in [26] that was limited to idealized pointmass models and lacked a feedback control.

math.OC↗

arXiv2026

Irreversible Port-Hamiltonian Formulations for 1-Dimensional fluid systems

The Irreversible Port-Hamiltonian Systems (IPHS) framework is extended to the modelling of non-isentropic fluids with viscous dissipation in the Eulerian description. Building on earlier IPHS formulations for diffusion-driven and non-convective distributed systems, it is shown that convective transport can be consistently encompassed by the framework by modifying the underlying differential operators. After revisiting the constitutive relations of non-isentropic fluids in both Eulerian and Lagrangian coordinates, it is demonstrate how these systems fit within an extended IPHS formulation. Furthermore, an extended parametrisation of the boundary port variables which ensures that the first and second laws of Thermodynamics are fulfilled allows to define a general class of boundary controlled IPHS.

physics.flu-dyn↗

arXiv2026

Conduction-Diffusion in N-Dimensional settings as irreversible port-Hamiltonian systems

This work extends previous 1D irreversible port-Hamiltonian system (IPHS) formulations to boundary-controlled ND distributed parameter systems describing conduction-diffusion fluid phenomena. Within a unified and thermodynamically consistent framework, we show that conduction and diffusion can be represented through a single coherent structure that preserves global energy balance and ensures a correct characterization of entropy production. The resulting formulation provides a foundation for the systematic modeling and control of complex multi-physical processes governed by coupled transport mechanisms in N dimensions. In the longer term, this framework opens the door to structure-preserving numerical schemes capable of enforcing thermodynamic principles directly at the discretized level.

eess.SY↗

arXiv2025

Structure preserving discretization method for 1D and 2D port-Hamiltonian systems using finite differences on staggered grids

This paper extends previous work on finitedifference schemes over staggered grids for infinite-dimensional port-Hamiltonian systems. In the one-dimensional setting, it generalizes the discretization approach originally developed for the wave equation to a broader class of systems characterized by interconnection operators that include both differential and non-differential terms, such as the Timoshenko beam equation. The paper then introduces a discretization strategy for the two-dimensional case that requires only two grids, thereby accommodating a wider range of systems, including those whose interconnection operators contain non-differential components, such as the Mindlin plate model.

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

Port-Hamiltonian modeling and control of a curling HASEL actuator

This paper is concerned with the modeling and control of a curling Hydraulically Amplified Self-healing Electrostatic (HASEL) actuator using the port-Hamiltonian (PH) approach. For that purpose, we use a modular approach and consider the HASEL actuator as an interconnection of elementary subsystems. Each subsystem is modeled by an electrical component consisting of a capacitor in parallel with an inductor connected through the conservation of volume of the moving liquid to a mechanical structure based on inertia, linear, and torsional springs. The parameters are then identified, and the model is validated on the experimental setup. Position control is achieved by using Interconnection and Damping Assignment-Passivity Based Control (IDA-PBC) with integral action (IA) for disturbance rejection. Simulation results show the efficiency of the proposed controller.

math.DS↗

arXiv2023

Port-Hamiltonian modeling of multidimensional flexible mechanical structures defined by linear elastic relations $\star$

This article presents a systematic methodology for modeling a class of flexible multidimensional mechanical structures defined by linear elastic relations that directly allows to obtain their infinite-dimensional port-Hamiltonian representation. The approach is restricted to systems based on a certain class of kinematic assumptions. However this class encompasses a wide range of models currently available in the literature, such as ${\ell}$-dimensional elasticity models (with ${\ell}$ = 1,2,3), vibrating strings, torsion in circular bars, classical beam and plate models, among others. The methodology is based on Hamilton's principle for a continuum medium which allows defining the energy variables of the port-Hamiltonian system, and also on a generalization of the integration by parts theorem, which allows characterizing the skew-adjoint differential operator and boundary inputs and boundary outputs variables. To illustrate this method, the plate modeling process based on Reddy's third-order shear deformation theory is presented as an example. To the best of our knowledge, this is the first time that an infinite-dimensional port-Hamiltonian representation of this system is presented in the literature.

math.DS↗

arXiv2023

Infinite-dimensional observers for high order boundary-controlled port-Hamiltonian systems

This letter investigates the design of a class of infinite-dimensional observers for one dimensional (1D) boundary controlled port-Hamiltonian systems (BC-PHS) defined by differential operators of order $N \geq 1$. The convergence of the proposed observer depends on the number and location of available boundary measurements. \textcolor{hector}{Asymptotic convergence is assured for $N\geq 1$, and provided that enough boundary measurements are available, exponential convergence can be assured for the cases $N=1$ and $N=2$.} Furthermore, in the case of partitioned BC-PHS with $N=2$, such as the Euler-Bernoulli beam, \textcolor{hector}{it is shown} that exponential convergence can be assured considering less available measurements. The Euler-Bernoulli beam model is used to illustrate the design of the proposed observers and to perform numerical simulations.

eess.SY↗

arXiv2023

Reduced order in domain control of distributed parameter port-Hamiltonian systems via energy shaping

An in-domain finite dimensional controller for a class of distributed parameter systems on a one-dimensional spatial domain formulated under the port-Hamiltonian framework is presented. Based on [25] where positive feedback and a late lumping approach are used, we extend the Control by Interconnection method and propose a new energy shaping methodology with an early lumping approach on the distributed spatial domain of the system. Our two main control objectives are to stabilize the closed loop system, as well as to improve the closed loop dynamic performances. With the early lumping approach, we investigate two cases of the controller design, the ideal case where each distributed controller acts independently on the spatial domain (fully-actuated), and the more realistic case where the controller is piecewise constant over certain interval (under-actuated). We then analyze the asymptotic stability of the closed loop system when the infinite dimensional plant system is connected with the finite dimensional controller. Furthermore we provide simulation results comparing the performance of the fully-actuated case and the under-actuated case with an example of an elastic vibrating string.

math.OC↗

arXiv2022

Observer-based boundary control of distributed port-Hamiltonian systems

An observer-based boundary controller for infinite-dimensional port-Hamiltonian systems defined on 1D spatial domains is proposed. The design is based on an early-lumping approach in which a finite-dimensional approximation of the infinite-dimensional system derived by spatial discretization is used to design the observer and the controller. As long as the finite-dimensional approximation approaches the infinite-dimensional model, the performances also do. The main contribution is a constructive method which guarantees that the interconnection between the controller and the infinite-dimensional system is asymptotically stable. A Timoshenko beam model has been used to illustrate the approach.

eess.SY↗

arXiv2022

Linear Matrix Inequality Design of Exponentially Stabilizing Observer-Based State Feedback Port-Hamiltonian Controllers

The design of an observer-based state feedback (OBSF) controller with guaranteed passivity properties for port-Hamiltonian systems (PHS) is addressed using linear matrix inequalities (LMIs). The observer gain is freely chosen and the LMIs conditions such that the state feedback is equivalent to control by interconnection with an input strictly passive (ISP) and/or an output strictly passive (OSP) and zero state detectable (ZSD) port-Hamiltonian controller are established. It is shown that the proposed controller exponentially stabilizes a class of infinite-dimensional PHS and asymptotically stabilizes a class of finite-dimensional non-linear PHS. A Timoshenko beam model and a microelectromechanical system are used to illustrate the proposed approach.

eess.SY↗

arXiv2022

A Lyapunov approach for the exponential stability of a damped Timoshenko beam

In this technical note, we consider the stability properties of a viscously damped Timoshenko beam equation with spatially varying parameters. With the help of the port-Hamiltonian framework, we first prove the existence of solutions and show, by an appropriate Lyapunov function, that the system is exponentially stable and has an explicit decay rate. The explicit exponential bound is computed for an illustrative example of which we provide some numerical simulations.

math.OC↗