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Loïc Michel

Publications and source records attributed to Loïc Michel.

14 recordsLinked to original sources
arXiv2026

Model-Free Based Computations of Recursive Control Barrier Function: Ultra-Local Model Approach

Control barrier functions (CBFs) provide a systematic framework for enforcing safety constraints in nonlinear control systems. However, their implementation typically relies on accurate system models, which can limit their applicability in the presence of significant modeling uncertainties or unknown dynamics. This paper proposes a model-free framework for the computation of recursive control barrier functions based on the ultra-local model approach that leverages online estimation of the unknown system dynamics to construct CBF constraints. This approach does not require an explicit model of the system dynamics and enhances robustness with respect to disturbances and model mismatch. The resulting control architecture enables the enforcement as well as the anticipation of safety constraints for systems with higher relative degree. The effectiveness of the proposed approach is illustrated on the adaptive cruise control benchmark.

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arXiv2025

A variational and symplectic framework for model-free control: preliminary results

The model-free control approach is an advanced control law that requires few information about the process to control. Since its introduction in 2008, numerous applications have been successfully considered, highlighting attractive robustness properties towards tracking efficiency and disturbance rejection. In this work, a variational approach of the model-free control is proposed in order to extend its robustness capabilities. An adaptive formulation of the controller is proposed using the calculus of variations within a symplectic framework, that aims to consider the control law as an optimization problem toward the auto-tuning of its main key parameter. The proposed formulation provides a coupling between the model-free control law and a variational integrator to improve the robustness of the tracking towards process changes and emphasize closed-loop stabilization. Some illustrative examples are discussed to highlight the rightness of the proposed approach.

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arXiv2024

A note about high-order semi-implicit differentiation: application to a numerical integration scheme with Taylor-based compensated error

In this brief, we discuss the implementation of a third order semi-implicit differentiator as a complement of the recent work by the author that proposes an interconnected semi-implicit Euler double differentiators algorithm through Taylor expansion refinement. The proposed algorithm is dual to the interconnected approach since it offers alternative flexibility to be tuned and to be implemented in real-time processes. In particular, an application to a numerical integration scheme is presented as the Taylor refinement can be of interest to improve the global convergence. Numerical results are presented to support the rightness of the proposed method.

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arXiv2021

Model-free based control of a HIV/AIDS prevention model

Controlling an epidemiological model is often performed using optimal control theory techniques for which the solution depends on the equations of the control system, objective functional and possible state and/or control constraints. In this paper, we propose a model-free control approach based on an algorithm that operates in 'real-time' and drives the state solution according to a direct feedback on the state solution that is aimed to be minimized, and without knowing explicitly the equations of the control system. We consider a concrete epidemic problem of minimizing the number of HIV infected individuals, through the preventive measure pre-exposure prophylaxis (PrEP) given to susceptible individuals. The solutions must satisfy control and mixed state-control constraints that represent the limitations on PrEP implementation. Our model-free based control algorithm allows to close the loop between the number of infected individuals with HIV and the supply of PrEP medication 'in real time', in such manner that the number of infected individuals is asymptotically reduced and the number of individuals under PrEP medication is below a fixed constant value. We prove the efficiency of our approach and compare the model-free control solutions with the ones obtained using a classical optimal control approach via Pontryagin maximum principle. The performed numerical simulations allow us to conclude that the model-free based control strategy highlights new and interesting performances compared with the classical optimal control approach.

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arXiv2021

Online learning of neural networks based on a model-free control algorithm

We explore the possibilities of using a model-free-based control law in order to train artificial neural networks. In the supervised learning context, we consider the problem of tuning the synaptic weights as a feedback control tracking problem where the control algorithm adjusts the weights online according to the input-output training data set of the neural network. Numerical results illustrate the dynamical learning process and an example of classifier that show very promising properties of our proposed approach.

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arXiv2018

A para-model agent for dynamical systems

Consider a dynamical system $u \mapsto x, \dot{x} = f_{nl}(x,u)$ where $f_{nl}$ is a nonlinear (convex or nonconvex) function, or a combination of nonlinear functions that can eventually switch. We present, in this preliminary work, a generalization of the standard model-free control, that can either control the dynamical system, given an output reference trajectory, or optimize the dynamical system as a derivative-free optimization based "extremum-seeking" procedure. Multiple applications are presented and the robustness of the proposed method is studied in simulation.

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arXiv2017

Model-Free Based Digital Control for Magnetic Measurements

This paper presents a novel digital control strategy successfully implemented for a soft magnetic material characterization bench (Epstein frame type). The main objective is to control the magnetic induction waveform whatever the applied excitation and the material under study. Given the nonlinear nature of the magnetization curves of magnetic materials, an original model-free based control technique is considered. Special mention should be made of the interesting dynamic properties in closed-loop against the changes of the operating point related basically to the hysteresis form. The operation and the performances of the digital control method are illustrated in different working conditions through both simulation and experimental measurements.

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arXiv2015

Algebraic-based nonstandard time-stepping schemes

In this preliminary work, we present nonstandard time-stepping strategies to solve differential equations based on the algebraic estimation method applied to the estimation of time-derivative, which provides interesting properties of "internal" filtering. We consider firstly a classical finite difference method, like the explicit Euler method for which we study the possibility of using the algebraic estimation of derivatives instead of the usual finite difference to compute the numerical derivation. Then, we investigate how to use the algebraic estimation of derivatives in order to improve the slope predictions in RK-based schemes.

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arXiv2014

Bernstein-based polynomial approach to study the stability of switched systems and formal verification using HOL Light

In this preliminary work, we propose to use a polynomial approach in order to study the stability of switched systems. The proposed strategy is based on the Bernstein interpolation method that may transform a switched system into a polynomial expression from which an associated "simple" Lyapunov function can be eventually built. The HOL Light proof assistant allows verifying formally the Lyapunov functions that are identified from the proposed switching structure. Our approach is illustrated by numerical examples.

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arXiv2014

Semi-explicit Parareal method based on convergence acceleration technique

The Parareal algorithm is used to solve time-dependent problems considering multiple solvers that may work in parallel. The key feature is a initial rough approximation of the solution that is iteratively refined by the parallel solvers. We report a derivation of the Parareal method that uses a convergence acceleration technique to improve the accuracy of the solution. Our approach uses firstly an explicit ODE solver to perform the parallel computations with different time-steps and then, a decomposition of the solution into specific convergent series, based on an extrapolation method, allows to refine the precision of the solution. Our proposed method exploits basic explicit integration methods, such as for example the explicit Euler scheme, in order to preserve the simplicity of the global parallel algorithm. The first part of the paper outlines the proposed method applied to the simple explicit Euler scheme and then the derivation of the classical Parareal algorithm is discussed and illustrated with numerical examples.

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arXiv2013

Model-free control of microgrids

A new "model-free" control methodology is applied for the first time to power systems included in microgrids networks. We evaluate its performances regarding output load and supply variations in different working configuration of the microgrid. Our approach, which utilizes "intelligent" PI controllers, does not require any converter or microgrid model identification while ensuring the stability and the robustness of the controlled system. Simulations results show that with a simple control structure, the proposed control method is almost insensitive to fluctuations and large load variations.

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arXiv2013

Model-free control of nonlinear power converters

A new "model-free" control methodology is applied to a boost power converter. The properties of the boost converter allow to evaluate the performances of the model-free strategy in the case of switching nonlinear transfer functions, regarding load variations. Our approach, which utilizes "intelligent" PI controllers, does not require any converter model identification while ensuring the stability and the robustness of the controlled system. Simulation results show that, with a simple control structure, the proposed control method is almost insensitive to fluctuations and large load variations.

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