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Experimental flight tests are reported about quadrotors UAVs via a recent model-free control (MFC) strategy, which is easily implementable. We show that it is possible to achieve acrobatic rate control of the UAV, which is beyond the previous standard. The same remote controller is tested on two physical vehicles without any re-tuning. It produces in both cases low tracking error. We show that MFC is robust even when the quadrotor is highly damaged. A video footage can be found at: https://youtu.be/wtSLalA4szc, 9th International Conference on Advanced Technologies (ICAT'20), 10-12 August 2020, Istanbul, Turkey

Cascade P-PI control systems are the most widespread commercial solutions for machine tool positioning systems. However, friction, backlash and wearing effects significantly degrade their closed-loop behaviour. This works proposes a novel easy-to-tune control approach that achieves high accuracy trajectory tracking in a wide operation domain, thus being able to mitigate wear and aging effects., This work is partially supported by the joint CNRS (France) - CSIC (Spain) PICS Program through the project UbiMFC (CoopIntEer 203 073).

In cloud computing management, the dynamic adaptation of computing resource allocations under time-varying workload is an active domain of investigation. Several control strategies were already proposed. Here the model-free control setting and the corresponding "intelligent" controllers, which are most successful in many concrete engineering situations, are employed for the "horizontal elasticity." When compared to the commercial "Auto-Scaling" algorithms, our easily implementable approach, behaves better even with sharp workload fluctuations. This is confirmed by experiments on Amazon Web Services (AWS)., in French

In today's literature "Model-Free Control," or MFC, and "Active Disturbance Rejection Control," or ADRC, are the most prominent approaches in order to keep the benefits of PID controllers, that are so popular in the industrial world, and in the same time for attenuating their severe shortcomings. After a brief review of MFC and ADRC, several examples show the superiority of MFC, which permits to tackle most easily a much wider class of systems., in French

This communication presents a longitudinal model-free control approach for computing the wheel torque command to be applied on a vehicle. This setting enables us to overcome the problem of unknown vehicle parameters for generating a suitable control law. An important parameter in this control setting is made time-varying for ensuring finite-time stability. Several convincing computer simulations are displayed and discussed. Overshoots become therefore smaller. The driving comfort is increased and the robustness to time-delays is improved., IFAC 2017 World Congress, Toulouse

An elementary mathematical example proves, thanks to the Routh-Hurwitz criterion, a result that is intriguing with respect to today's practical understanding of model-free control, i.e., an "intelligent" proportional controller (iP) may turn to be more difficult to tune than an intelligent proportional-derivative one (iPD). The vast superiority of iPDs when compared to classic PIDs is shown via computer simulations. The introduction as well as the conclusion analyse model-free control in the light of recent advances., in French, https://www.openscience.fr/Un-resultat-intrigant-en-commande-sans-modele

The recent popularity of post-denitrification processes in the greater Paris area wastewater treatment plants has caused a resurgence of the presence of nitrite in the Seine river. Controlling the production of nitrite during the post-denitrification has thus become a major technical issue. Research studies have been led in the MOCOPEE program (www.mocopee.com) to better understand the underlying mechanisms behind the production of nitrite during wastewater denitrification and to develop technical tools (measurement and control solutions) to assist on-site reductions of nitrite productions. Prior studies have shown that typical methanol dosage strategies produce a varying carbon-to-nitrogen ratio in the reactor, which in turn leads to unstable nitrite concentrations in the effluent. The possibility of adding a model-free control to the actual classical dosage strategy has thus been tested on the SimBio model, which simulates the behavior of wastewater biofilters. The corresponding "intelligent" feedback loop, which is using effluent nitrite concentrations, compensates the classical strategy only when needed. Simulation results show a clear improvement in average nitrite concentration level and level stability in the effluent, without a notable overcost in methanol., in french, Journal of Water Science, to appear

Recent investigations on the longitudinal and lateral control of wheeled autonomous vehicles are reported. Flatness-based techniques are first introduced via a simplified model. It depends on some physical parameters, like cornering stiffness coefficients of the tires, friction coefficient of the road, ..., which are notoriously difficult to identify. Then a model-free control strategy, which exploits the flat outputs, is proposed. Those outputs also depend on physical parameters which are poorly known, i.e., the vehicle mass and inertia and the position of the center of gravity. A totally model-free control law is therefore adopted. It employs natural output variables, namely the longitudinal velocity and the lateral deviation of the vehicle. This last method, which is easily understandable and implementable, ensures a robust trajectory tracking problem in both longitudinal and lateral dynamics. Several convincing computer simulations are displayed., 9th IFAC Symposium on Intelligent Autonomous Vehicles (Leipzig, Germany, 29.06.2016 - 01.07.2016)

Systematic and multifactor risk models are revisited via methods which were already successfully developed in signal processing and in automatic control. The results, which bypass the usual criticisms on those risk modeling, are illustrated by several successful computer experiments., Comment: First Paris Financial Management Conference, Paris : France (2013)

International audience; It is shown that the "intelligent" controllers which are associated to the recently introduced model-free control synthesis may be easily implemented on cheap and small programmable devices. Several successful numerical experiments are presented with a special emphasis on fault tolerant control.

"Model-free" control and the related "intelligent" proportional-integral (PI) controllers are successfully applied to freeway ramp metering control. Implementing moreover the corresponding control strategy is straightforward. Numerical simulations on the other hand need the identification of quite complex quantities like the free flow sp\^eed and the critical density. This is achieved thanks to new estimation techniques where the differentiation of noisy signals plays a key r\^ole. Several excellent computer simulations are provided and analyzed., Comment: 13th IFAC Symposium on Control in Transportation Systems (CTS 2012), Sofia : Bulgaria (2012)

The experience gained with numerous successful applications permits to revisit some points of model-free control. The numerical differentiation of noisy signals may be replaced by a real time parameter identification which is much simpler. The strange ubiquity of classic PIDs is explained as well as the almost universal utilization of ultra-local models of order 1. We show that even with a partially known model the utilization of an intelligent PI controller remains profitable. Two examples, an inverted pendulum and a heat exchanger, seem to confirm the superiority of model-free control with respect to sliding modes control and techniques stemming from infinite-dimensional systems, such as delays or partial differential equations. Our paper is illustrated by several computer simulations.

International audience; The ubiquity of PID controllers in the industry has remained mysterious until now. We provide here a mathematical explanation of this strange phenomenon by comparing their sampling with the the one of "intelligent'' PID controllers, which were recently introduced. Some computer simulations nevertheless confirm the superiority of the new intelligent feedback design.

A new concept called "Model-Free Control" is applied to hydroelectric run-of-the river power plants, with severe constraints and operating conditions. Numerous computer simulations display excellent results, which are obtained thanks to simple and robust algorithms.

International audience; We are settling a longstanding quarrel in quantitative finance by proving the existence of trends in financial time series thanks to a theorem due to P. Cartier and Y. Perrin, which is expressed in the language of nonstandard analysis (Integration over finite sets, F. & M. Diener (Eds): Nonstandard Analysis in Practice, Springer, 1995, pp. 195--204). Those trends, which might coexist with some altered random walk paradigm and efficient market hypothesis, seem nevertheless difficult to reconcile with the celebrated Black-Scholes model. They are estimated via recent techniques stemming from control and signal theory. Several quite convincing computer simulations on the forecast of various financial quantities are depicted. We conclude by discussing the rôle of probability theory.

The signal to noise ratio, which plays such an important r��le in information theory, is shown to become pointless for digital communications where the demodulation is achieved via new fast estimation techniques. Operational calculus, differential algebra, noncommutative algebra and nonstandard analysis are the main mathematical tools.

The signal to noise ratio, which plays such an important role in information theory, is shown to become pointless in digital communications where - symbols are modulating carriers, which are solutions of linear differential equations with polynomial coefficients, - demodulations is achieved thanks to new algebraic estimation techniques. Operational calculus, differential algebra and nonstandard analysis are the main mathematical tools.

This note is sketching a simple and natural mathematical construction for explaining the probabilistic nature of quantum mechanics. It employs nonstandard analysis and is based on Feynman's interpretation of the Heisenberg uncertainty principle, i.e., of the quantum fluctuations, which was brought to the forefront in some fractal approaches. It results, as in Nelson's stochastic mechanics, in stochastic differential equations which are deduced from infinitesimal random walks. An extended english abstract gives most of the details.

A control strategy without any precise mathematical model is derived for linear or nonlinear systems which are assumed to be finite-dimensional. Two convincing numerical simulations are provided.

This note is answering an old questioning about the F��nyes-Nelson stochastic mechanics. The Brownian nature of the quantum fluctuations, which are associated to this mechanics, is deduced from Feynman's interpretation of the Heisenberg uncertainty principle via infinitesimal random walks stemming from nonstandard analysis. It is therefore no more necessary to combine those fluctuations with a background field, which has never been well understood. Most of the technical details are contained in an extended english abstract.

New definitions are suggested for frequencies which may be instantaneous or not. The Heisenberg-Gabor inequality and the Shannon sampling theorem are briefly discussed.

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., Comment: 10th Vienna International Conference on Mathematical Modelling (MATHMOD 2022) -- July 27-29, 2022 -- Vienna, Austria