arXiv subjects

Michel Fliess

Publications and source records attributed to Michel Fliess.

At least 19 recordsLinked to original sources

arXiv2026

Model-Free Detection and Accommodation of Sensor Faults for a PEM Electrolyzer

We investigate the detection and accommodation of sensor faults for a proton exchange membrane electrolyzer coupled to a DC/DC converter powered by renewable energy sources. The proposed method for detecting and accommodating the sensor fault is model-free and is based on the concept of ultra-local model that is becoming classic in control engineering. The existing literature on active control tolerant to sensor fault dedicated to this question shows that no previous work has addressed this topic. Our approach mitigates the effect of sensor fault on closed-loop behavior and guarantees the stability and performance of the overall system. Numerical simulations under variations in renewable energy sources validate our approach.

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arXiv2026

Air supply control for proton exchange membrane fuel cells without explicit modeling

Our objective is to study the performance and robustness of the model-free strategy for controlling the oxygen stoichiometry of a fuel cell air supply system with a proton exchange membrane. After reviewing the literature on modeling and control of this process, the model-free approach appears to be a good candidate because, on the one hand, it allows straightforward real-time adaptation to track operating points and, on the other hand, it requires a low computational burden, which is attractive for industrial applications. Numerical simulations for two scenarios (constant and variable oxygen stoichiometry) with two current profiles reveal satisfactory performance of the model-free control law. The robustness is addressed by considering significant variations in the parameters of the proton exchange membrane air supply system.

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arXiv2026

A flatness proof of the exponential turnpike phenomenon for linear-quadratic optimal control problems

We revisit finite-dimensional linear-quadratic optimal control from the viewpoint of differential flatness. If the pair (A, B) is controllable, then the linear control system is flat, and every trajectory can be parametrized by a flat output and finitely many of its derivatives. Once this parametrization is inserted into the quadratic functional, the Euler-Lagrange condition becomes a linear differential equation with constant coefficients, or more generally a polynomial matrix differential equation. After reduction to Smith normal form, this equation decouples into scalar constant-coefficient equations, and its solutions are exponentialpolynomials. This yields a viewpoint on the turnpike phenomenon that is quite different from the classical Hamiltonian-Riccati analysis: the turnpike mechanism appears directly from the stable-unstable splitting of the reduced flat equation. In particular, when the reduced Euler-Lagrange operator has no purely imaginary characteristic roots and when the endpoint constraints act nondegenerately on the stable and unstable modes, the optimal trajectory consists of a left-boundary layer, a right-boundary layer, and a long interior arc exponentially close to the static optimum. The same viewpoint also clarifies what changes when some weights are only semidefinite: the order of the reduced equation may drop, some endpoint conditions may become incompatible, and polynomial or oscillatory modes may destroy the exponential turnpike. It also gives a natural meaning to certain endpoint constraints on the control and on finitely many derivatives of the control: such traces are not defined on the ambient L 2 control space, but they are meaningful on the smooth extremals selected by the reduced Euler-Lagrange equation. We formulate this principle as a general theorem and illustrate it in detail on the double integrator.

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arXiv2026

Sterile mosquito release via intelligent proportional controllers

The Sterile Insect Technique (SIT) against insect pests and insect vectors consists of releasing males that have been previously sterilized in order to reduce or eliminate a specific wild population. We study this complex control question via model-free control, ultra-local models, and intelligent proportional controllers that have already proven their effectiveness in various fields. They permit addressing, perhaps for the first time, the essential sampling question. Computer simulations are displayed and discussed.

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arXiv2025

Linear Quadratic Regulators: A New Look

Linear time-invariant control systems can be considered as finitely generated modules over the commutative principal ideal ring $\mathbb{R}[\frac{d}{dt}]$ of linear differential operators with respect to the time derivative. The Kalman controllability in this algebraic language is translated as the freeness of the system module. Linear quadratic regulators rely on quadratic Lagrangians, or cost functions. Any flat output, i.e., any basis of the corresponding free module leads to an open-loop control strategy via an Euler-Lagrange equation, which becomes here a linear ordinary differential equation with constant coefficients. In this approach, the two-point boundary value problem, including the control variables, becomes tractable. It yields notions of optimal time horizon, optimal parameter design and optimal rest-to-rest trajectories. The loop is closed via an intelligent controller derived from model-free control, which is known to exhibit excellent performance concerning model mismatches and disturbances.

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arXiv2025

Avoidance of an unexpected obstacle without reinforcement learning: Why not using advanced control-theoretic tools?

This communication on collision avoidance with unexpected obstacles is motivated by some critical appraisals on reinforcement learning (RL) which "requires ridiculously large numbers of trials to learn any new task" (Yann LeCun). We use the classic Dubins' car in order to replace RL with flatness-based control, combined with the HEOL feedback setting, and the latest model-free predictive control approach. The two approaches lead to convincing computer experiments where the results with the model-based one are only slightly better. They exhibit a satisfactory robustness with respect to randomly generated mismatches/disturbances, which become excellent in the model-free case. Those properties would have been perhaps difficult to obtain with today's popular machine learning techniques in AI. Finally, we should emphasize that our two methods require a low computational burden.

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arXiv2025

Disruption of parkinsonian brain oscillations

Deep brain stimulation (DBS) is an advanced surgical treatment for the symptoms of Parkinson's disease (PD), involving electrical stimulation of neurons within the basal ganglia region of the brain. DBS is traditionally delivered in an open-loop manner using fixed stimulation parameters, which may lead to suboptimal results. In an effort to overcome these limitations, closed loop DBS, using pathological subthalamic beta (13--30 Hz) activity as a feedback signal, offers the potential to adapt DBS automatically in response to changes in patient symptoms and side effects. However, clinically implemented closed-loop techniques have been limited to date to simple control algorithms, due to the inherent uncertainties in the dynamics involved. Model-free control, which has already seen successful applications in the field of bioengineering, offers a way to avoid this limitation and provides an alternative method to apply modern control approach to selective suppression of pathological oscillations.

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arXiv2025

Guidance and Control of Unmanned Surface Vehicles via HEOL

This work presents a new approach to the guidance and control of marine craft via HEOL, i.e., a new way of combining flatness-based and model-free controllers. Its goal is to develop a general regulator for Unmanned Surface Vehicles (USV). To do so, the well-known USV maneuvering model is simplified into a nominal Hovercraft model which is flat. A flatness-based controller is derived for the simplified USV model and the loop is closed via an intelligent proportional-derivative (iPD) regulator. We thus associate the well-documented natural robustness of flatness-based control and adaptivity of iPDs. The controller is applied in simulation to two surface vessels, one meeting the simplifying hypotheses, the other one being a generic USV of the literature. It is shown to stabilize both systems even in the presence of unmodeled environmental disturbances.

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arXiv2025

Model-Free Predictive Control: Introductory Algebraic Calculations, and a Comparison with HEOL and ANNs

Model predictive control (MPC) is a popular control engineering practice, but requires a sound knowledge of the model. Model-free predictive control (MFPC), a burning issue today, also related to reinforcement learning (RL) in AI, is reformulated here via a linear differential equation with constant coefficients, thanks to a new perspective on optimal control combined with recent advances in the field of model-free control (MFC). It is replacing Dynamic Programming, the Hamilton-Jacobi-Bellman equation, and Pontryagin's Maximum Principle. The computing burden is low. The implementation is straightforward. Two nonlinear examples, a chemical reactor and a two tank system, are illustrating our approach. A comparison with the HEOL setting, where some expertise of the process model is needed, shows only a slight superiority of the later. A recent identification of the two tank system via a complex ANN architecture might indicate that a full modeling and the corresponding machine learning mechanism are not always necessary neither in control, nor, more generally, in AI.

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arXiv2025

Synchronization of Kuramoto oscillators via HEOL, and a discussion on AI

Artificial neural networks and their applications in deep learning have recently made an incursion into the field of control. Deep learning techniques in control are often related to optimal control, which relies on Pontryagin maximum principle or the Hamilton-Jacobi-Bellman equation. They imply control schemes that are tedious to implement. We show here that the new HEOL setting, resulting from the fusion of the two established approaches, namely differential flatness and model-free control, provides a solution to control problems that is more sober in terms of computational resources. This communication is devoted to the synchronization of the popular Kuramoto's coupled oscillators, which was already considered via artificial neural networks (Böttcher et al., Nature Communications 2022), where, contrarily to this communication, only the single control variable is examined. One establishes the flatness of Kuramoto's coupled oscillator model with multiplicative control and develops the resulting HEOL control. Unlike many exemples, this system reveals singularities that are avoided by a clever generation of phase angle trajectories. The results obtained, verified in simulation, show that it is not only possible to synchronize these oscillators in finite time, and even to follow angular frequency profiles, but also to exhibit robustness concerning model mismatches. To the best of our knowledge this has never been done before. Concluding remarks advocate a viewpoint, which might be traced back to Wiener's cybernetics: control theory belongs to AI.

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arXiv2024

The Euler-Lagrange equation and optimal control: Preliminary results

Algebraically speaking, linear time-invariant (LTI) systems can be considered as modules. In this framework, controllability is translated as the freeness of the system module. Optimal control mainly relies on quadratic Lagrangians and the consideration of any basis of the system module leads to an open-loop control strategy via a linear Euler-Lagrange equation. In this approach, the endpoint is easily assignable and time horizon can be chosen to minimize the criterion. The loop is closed via an intelligent controller derived from model-free control, which exhibits excellent performances concerning model mismatches and disturbances. The extension to nonlinear systems is briefly discussed.

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arXiv2024

Detection and suppression of epileptiform seizures via model-free control and derivatives in a noisy environment

Recent advances in control theory yield closed-loop neurostimulations for suppressing epileptiform seizures. These advances are illustrated by computer experiments which are easy to implement and to tune. The feedback synthesis is provided by an intelligent proportional-derivative (iPD) regulator associated to model-free control. This approach has already been successfully exploited in many concrete situations in engineering, since no precise computational modeling is needed. iPDs permit tracking a large variety of signals including high-amplitude epileptic activity. Those unpredictable pathological brain oscillations should be detected in order to avoid continuous stimulation, which might induce detrimental side effects. This is achieved by introducing a data mining method based on the maxima of the recorded signals. The real-time derivative estimation in a particularly noisy epileptiform environment is made possible due to a newly developed algebraic differentiator. The virtual patient is the Wendling model, i.e., a set of ordinary differential equations adapted from the Jansen-Rit neural mass model in order to generate epileptiform activity via appropriate values of excitation- and inhibition-related parameters. Several simulations, which lead to a large variety of possible scenarios, are discussed. They show the robustness of our control synthesis with respect to different virtual patients and external disturbances.

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arXiv2024

Flatness-based control revisited: The HEOL setting

We present the algebraic foundations of the HEOL setting, which combines flatness-based control and intelligent controllers, two advances in automatic control that have been proven in practice, including in industry. The result provides a solution to many pending questions on feedback loops concerning flatness-based control and model-free control (MFC). Elementary module theory, ordinary differential fields and the generalization of Kähler differentials to differential fields provide an intrinsic definition of the tangent linear system. The algebraic manipulations associated with the operational calculus lead to homeostat and intelligent controllers. They are illustrated via some computer simulations.

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arXiv2023

A control-theoretic simplification of adaptive bitrate (ABR) video streaming

Adaptive bitrate streaming (ABR) over the HyperText Transfer Protocol (HTTP), which raises numerous delicate questions, is nowadays almost the only approach to video streaming. This paper presents elementary solutions to three key issues: 1) A straightforward feedforward control strategy for the bitrate and the buffer level via flatness-based control. 2) Closing the loop permits mitigating unavoidable mismatches and disturbances, such as Internet fluctuations. This is adapted from the new HEOL setting, which mixes model-free and flatness-based controls. 3) An easily implementable closed-form estimate of the bandwidth via algebraic identification techniques is derived, perhaps for the first time. It permits handling severe variations in channel capacity. Several computer experiments and metrics for evaluating the Quality of Experience (QoE) are displayed and discussed.

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arXiv2023

Active queue management for alleviating Internet congestion via a nonlinear differential equation with a variable delay

Active Queue Management (AQM) for mitigating Internet congestion has been addressed via various feedback control syntheses, especially P, PI, and PID regulators, by using a linear approximation where the ``round trip time'', i.e., the delay, is assumed to be constant. This constraint is lifted here by using a nonlinear modeling with a variable delay, introduced more than 20 years ago. This delay, intimately linked to the congestion phenomenon, may be viewed as a ``flat output.'' All other system variables, especially the control variable, i.e., the packet loss ratio, are expressed as a function of the delay and its derivatives: they are frozen if the delay is kept constant. This flatness-like property, which demonstrates the mathematical discrepancy of the linear approximation adopted until today, yields also our control strategy in two steps: Firstly, designing an open-loop control, thanks to straightforward flatness-based control techniques, and secondly, closing the loop via Model-Free Control (MFC) in order to take into account severe model mismatches, like, here, the number of TCP sessions. Several convincing computer simulations, which are easily implementable, are presented and discussed.

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arXiv2022

Active queue management: First steps toward a new control-theoretic viewpoint

Active Queue Management (AQM) for mitigating Internet congestion has been addressed via various feedback control syntheses, among which P, PI, and PID regulators are quite popular and often associated to a Smith predictor. Here, to better account for the many uncertainties, like the round trip time or the number of TCP sessions, the above controllers are replaced by an intelligent proportional controller associated to Model-Free Control (MFC) and by forecasting techniques derived from a new approach to time series. Several computer simulations via a well accepted linear modeling, where the delay is assumed to be constant, are presented and discussed.

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arXiv2022

Speed-Adaptive Model-Free Lateral Control for Automated Cars

In order to increase the number of situations in which an intelligent vehicle can operate without human intervention, lateral control is required to accurately guide it in a reference trajectory regardless of the shape of the road or the longitudinal speed. Some studies address this problem by tuning a controller for low and high speeds and including an output adaptation law. In this paper, a strategy framed in the Model-Free Control paradigm is presented to laterally control the vehicle over a wide speed range. Tracking quality, system stability and passenger comfort are thoroughly analyzed and compared to similar control structures. The results obtained both in simulation and with a real vehicle show that the developed strategy tracks a large number of trajectories with high degree of accuracy, safety and comfort.

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arXiv2022

Feedback control of social distancing for COVID-19 via elementary formulae

Social distancing has been enacted in order to mitigate the spread of COVID-19. Like many authors, we adopt the classic epidemic SIR model, where the infection rate is the control variable. Its differential flatness property yields ele mentary closed-form formulae for open-loop social distancing scenarios, where, for instance, the increase of the number of uninfected people may be taken into account. Those formulae might therefore be useful to decision makers. A feedback loop stemming from model-free control leads to a remarkable robustness with respect to severe uncertainties and mismatches. Although an identification procedure is presented, a good knowledge of the recovery rate is not necessary for our control strategy.

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