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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 K\"ahler 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., Comment: Accepted for publication in "Comptes Rendus Math\'ematique"

Combining flatness-based control, model-free control and algebraic estimation techniques permits to trivialize several key issues in the adaptive bitrate (ABR) setting, now the dominant industry approach in video streaming: 1) A straightforward open-loop strategy for the bitrate and the buffer level; 2) closing the loop permits not only to take into account unavoidable mismatches and disturbances, like Internet fluctuations, but also the inherently discrete nature of the bitrate; 3) an easily implementable closed-form estimate for a bandwidth allows to handle severe variations of the channel capacity. Several computer experiments and metrics for evaluating the Quality of Experience (QoE) are displayed and discussed.

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., Comment: Accepted for publication in "Annual Review in Control"

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., Comment: 10th International Conference on Systems and Control (ICSC'2022), Marseille, France, 23-25 November 2022

The aim of ramp metering is to improve the highway traffic conditions by an appropriate regulation of the inflow from the on-ramps to the highway mainstream. Our presentation rests on several improvements: 1) Our simulation techniques do not need contrarily to other approaches any heuristic fundamental law. 2) There is no need of crucial time-varying quantities, like the critical density, which is most difficult to estimate correctly online. 3) Our feedback loop, which is stemming from model-free control, is easy to implement and shows an excellent robustness with respect to model mismatch. Several computer experiments are displayed and discussed., Comment: 3rd DECOD (DElays and COnstraints in Distributed parameter systems) Workshop, 23-26 November 2021, Gif-sur-Yvette, France

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

We present some "in silico" experiments to design combined chemo- and immunotherapy treatment schedules. We introduce a new framework by combining flatness-based control, which is a model-based setting, along with model-free control. The flatness property of the used mathematical model yields straightforward reference trajectories. They provide us with the nominal open-loop control inputs. Closing the loop via model-free control allows to deal with the uncertainties on the injected drug doses. Several numerical simulations illustrating different case studies are displayed. We show in particular that the considered health indicators are driven to the safe region, even for critical initial conditions. Furthermore, in some specific cases there is no need to inject chemotherapeutic agents., Comment: IFAC Symposium on Biological and Medical Systems - 11th BMS 2021 -- Ghent, Belgium, 19-22 September 2021

Defense against cyberattacks is an emerging topic related to fault-tolerant control. In order to avoid difficult mathematical modeling, model-free control (MFC) is suggested as an alternative to classical control. For illustration purpose a Load Frequency Control of multi-areas power network is considered. In the simulations, load altering attacks and Denial of Service (DoS) in the communication network are applied to the system. Our aim is to compare the impact of cyberattacks on control loops closed via respectively a classical controller in such situations and a model-free one. Computer experiments show impressive results with MFC., Comment: 5th International Conference on Control and Fault-Tolerant Systems, Saint-Rapha\"{e}l, France, September 29th - October 1st, 2021

This paper suggests to replace PIs and PIDs, which play a key role in control engineering, by intelligent Proportional-Derivative feedback loops, or iPDs, which are derived from model-free control. This standpoint is enhanced by a laboratory experiment., Comment: Accepted in "International Journal of Robust and Nonlinear Control"

Although variable-speed three-blade wind turbines are nowadays quite popular, their control remains a challenging task. We propose a new easily implementable model-free control approach with the corresponding intelligent controllers. Several convincing computer simulations, including some fault accommodations, shows that model-free controllers are more efficient and robust than classic proportional-integral controllers., Comment: 4th European Conference on Electrical Engineering & Computer Science (EECS 2020), Bern (Switzerland), December 21-23, 2020

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, Comment: 9th International Conference on Advanced Technologies (ICAT'20), 10-12 August 2020, Istanbul, Turkey

This paper states that Model-Free Control (MFC), which must not be confused with Model-Free Reinforcement Learning, is a new tool for Machine Learning (ML). MFC is easy to implement and should be substituted in control engineering to ML via Artificial Neural Networks and/or Reinforcement Learning. A laboratory experiment, which was already investigated via today's ML techniques, is reported in order to confirm this viewpoint., Comment: FTC 2020 (Future Technologies Conference 2020) -- 5-6 November 2020, Vancouver, Canada

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., Comment: 21st IFAC World Congress, Berlin, Germany, July 12-17, 2020

Model-Free Control (MFC), which is easy to implement both from software and hardware viewpoints, permits the introduction of a high level control synthesis for the Industrial Internet of Things (IIoT) and the Industry 4.0. The choice of the User Diagram Protocol (UDP) as the Internet Protocol permits to neglect the latency. In spite of most severe packet losses, convincing computer simulations and laboratory experiments show that MFC exhibits a good Quality of Service (QoS) and behaves better than a classic PI regulator., Comment: 28th Mediterranean Conference on Control and Automation (MED'2020), 16-19 June, 2020 -- Saint-Rapha\"{e}l, France

The air conditioning management of data centers, a key question with respect to energy saving, is here tackled via the recent model-free control synthesis. Mathematical modeling becomes useless in this approach. The tuning of the corresponding intelligent proportional controller is straightforward. Computer simulations show excellent tracking performances in various realistic situations, like CPU load or temperature changes., Comment: International Conference on Control, Automation and Diagnosis (ICCAD'19), Grenoble, France, 2-4 July 2019

Supply chain management and inventory control provide most exciting examples of control systems with delays. Here, Smith predictors, model-free control and new time series forecasting techniques are mixed in order to derive an efficient control synthesis. Perishable inventories are also taken into account. The most intriguing "bullwhip effect" is explained and attenuated, at least in some important situations. Numerous convincing computer simulations are presented and discussed., Comment: 6th International Conference on Control, Decision and Information Technologies (CoDIT), Paris, April 2019

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)., Comment: 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., Comment: in French

"Dynamic compensation" is a robustness property where a perturbed biological circuit maintains a suitable output [Karin O., Swisa A., Glaser B., Dor Y., Alon U. (2016). Mol. Syst. Biol., 12: 886]. In spite of several attempts, no fully convincing analysis seems now to be on hand. This communication suggests an explanation via "model-free control" and the corresponding "intelligent" controllers [Fliess M., Join C. (2013). Int. J. Contr., 86, 2228-2252], which are already successfully applied in many concrete situations. As a byproduct this setting provides also a slightly different presentation of homeostasis, or "exact adaptation," where the working conditions are assumed to be "mild." Several convincing, but academic, computer simulations are provided and discussed., Comment: Research Report, Ecole polytechnique, Palaiseau, France

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., Comment: in french, Journal of Water Science, to appear

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., Comment: in French, https://www.openscience.fr/Un-resultat-intrigant-en-commande-sans-modele

The model-based control of building heating systems for energy saving encounters severe physical, mathematical and calibration difficulties in the numerous attempts that has been published until now. This topic is addressed here via a new model-free control setting, where the need of any mathematical description disappears. Several convincing computer simulations are presented. Comparisons with classic PI controllers and flatness-based predictive control are provided., Comment: 21st International Conference on System Theory, Control and Computing, October 2017, Sinaia, Romania

This paper presents a new model-free control (MFC) mechanism that enables the local distribution level circuit consumption of the photovoltaic (PV) generation by local building loads, in particular, distributed heating, ventilation and air conditioning (HVAC) units. The local consumption of PV generation will help minimize the impact of PV generation on the distribution grid, reduce the required battery storage capacity for PV penetration, and increase solar PV generation penetration levels. The proposed MFC approach with its corresponding intelligent controllers does not require any precise model for buildings, where a reliable modeling is a demanding task. Even when assuming the availability of a good model, the various building architectures would compromise the performance objectives of any model-based control strategy. The objective is to consume most of the PV generation locally while maintaining occupants comfort and physical constraints of HVAC units. That is, by enabling proper scheduling of responsive loads temporally and spatially to minimize the difference between demand and PV production, it would be possible to reduce voltage variations and two-way power flow. Computer simulations show promising results where a significant proportion of the PV generation can be consumed by building HVAC units with the help of intelligent control.

In this paper, the problem of tracking desired longitudinal and lateral motions for a vehicle is addressed. Let us point out that a "good" modeling is often quite difficult or even impossible to obtain. It is due for example to parametric uncertainties, for the vehicle mass, inertia or for the interaction forces between the wheels and the road pavement. To overcome this type of difficulties, we consider a model-free control approach leading to "intelligent" controllers. The longitudinal and the lateral motions, on one hand, and the driving/braking torques and the steering wheel angle, on the other hand, are respectively the output and the input variables. An important part of this work is dedicated to present simulation results with actual data. Actual data, used in Matlab as reference trajectories, have been previously recorded with an instrumented Peugeot 406 experimental car. The simulation results show the efficiency of our approach. Some comparisons with a nonlinear flatness-based control in one hand, and with a classical PID control in another hand confirm this analysis. Other virtual data have been generated through the interconnected platform SiVIC/RTMaps, which is a virtual simulation platform for prototyping and validation of advanced driving assistance systems., Comment: IEEE Transactions on Intelligent Transportation Systems

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., Comment: IFAC 2017 World Congress, Toulouse

Due to severe mathematical modeling and calibration difficulties open-loop feedforward control is mainly employed today for wastewater denitrification, which is a key ecological issue. In order to improve the resulting poor performances a new model-free control setting and its corresponding "intelligent" controller are introduced. The pitfall of regulating two output variables via a single input variable is overcome by introducing also an open-loop knowledge-based control deduced from the plant behavior. Several convincing computer simulations are presented and discussed., Comment: IFAC 2017 World Congress, Toulouse, France

Control of an inflammatory immune response is still an ongoing research. Here, a strategy consisting of manipulating a pro and anti-inflammatory mediator is considered. Already existing and promising model-based techniques suffer unfortunately from a most difficult calibration. This is due to the different types of inflammations and to the strong parameter variation between patients. This communication explores another route via the new model-free control and its corresponding "intelligent" controllers. A "virtual" patient, i.e., a mathematical model, is only employed for digital simulations. A most interesting feature of our control strategy is the fact that the two outputs which must be driven are sensorless. This difficulty is overcome by assigning suitable reference trajectories to two other outputs with sensors. Several most encouraging computer simulations, corresponding to different drug treatment strategies, are displayed and discussed., Comment: European Control Conference, Aalborg, Denmark, June 29 - July 1, 2016

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., Comment: 9th IFAC Symposium on Intelligent Autonomous Vehicles (Leipzig, Germany, 29.06.2016 - 01.07.2016)

A new model-free setting and the corresponding "intelligent" P and PD controllers are employed for the longitudinal and lateral motions of a vehicle. This new approach has been developed and used in order to ensure simultaneously a best profile tracking for the longitudinal and lateral behaviors. The longitudinal speed and the derivative of the lateral deviation, on one hand, the driving/braking torque and the steering angle, on the other hand, are respectively the output and the input variables. Let us emphasize that a "good" mathematical modeling, which is quite difficult, if not impossible to obtain, is not needed for such a design. An important part of this publication is focused on the presentation of simulation results with actual and virtual data. The actual data, used in Matlab as reference trajectories, have been obtained from a properly instrumented car (Peugeot 406). Other virtual sets of data have been generated through the interconnected platform SiVIC/RTMaps. It is a dedicated virtual simulation platform for prototyping and validation of advanced driving assistance systems. Keywords- Longitudinal and lateral vehicle control, model-free control, intelligent P controller (i-P controller), algebraic estimation, ADAS (Advanced Driving Assistance Systems)., Comment: in 14th European Control Conference, Jul 2015, Linz, Austria. 2015

Writing down mathematical models of agricultural greenhouses and regulating them via advanced controllers are challenging tasks since strong perturbations, like meteorological variations, have to be taken into account. This is why we are developing here a new model-free control approach and the corresponding intelligent controllers, where the need of a good model disappears. This setting, which has been introduced quite recently and is easy to implement, is already successful in many engineering domains. Tests on a concrete greenhouse and comparisons with Boolean controllers are reported. They not only demonstrate an excellent climate control, where the reference may be modified in a straightforward way, but also an efficient fault accommodation with respect to the actuators.

We show that the open-loop transfer functions and the stability margins may be defined within the recent model-free control setting. Several convincing computer experiments are presented including one which studies the robustness with respect to delays., Comment: 13th European Control Conference, Strasbourg : France (2014)

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 corresponding "intelligent" PID controllers (iPIDs), which already had many successful concrete applications, are presented here for the first time in an unified manner, where the new advances are taken into account. The basics of model-free control is now employing some old functional analysis and some elementary differential algebra. The estimation techniques become quite straightforward via a recent online parameter identification approach. The importance of iPIs and especially of iPs is deduced from the presence of friction. The strange industrial ubiquity of classic PID's and the great difficulty for tuning them in complex situations is deduced, via an elementary sampling, from their connections with iPIDs. Several numerical simulations are presented which include some infinite-dimensional systems. They demonstrate not only the power of our intelligent controllers but also the great simplicity for tuning them.

"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.

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.

Delta hedging, which plays a crucial r\^ole in modern financial engineering, is a tracking control design for a "risk-free" management. We utilize the existence of trends in financial time series (Fliess M., Join C.: A mathematical proof of the existence of trends in financial time series, Proc. Int. Conf. Systems Theory: Modelling, Analysis and Control, Fes, 2009. Online: http://hal.inria.fr/inria-00352834/en/) in order to propose a model-free setting for delta hedging. It avoids most of the shortcomings encountered with the now classic Black-Scholes-Merton framework. Several convincing computer simulations are presented. Some of them are dealing with abrupt changes, i.e., jumps., Comment: 18th Mediterranean Conference on Control and Automation, Marrakech : Morocco (2010)

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.

We are introducing a model-free control and a control with a restricted model for finite-dimensional complex systems. This control design may be viewed as a contribution to "intelligent" PID controllers, the tuning of which becomes quite straightforward, even with highly nonlinear and/or time-varying systems. Our main tool is a newly developed numerical differentiation. Differential algebra provides the theoretical framework. Our approach is validated by several numerical experiments., Comment: This communication is a slightly modified and updated version of a paper by the same authors (Commande sans mod\`ele et commande \`a mod\`ele restreint, e-STA, vol. 5 (\degree 4), pp. 1-23, 2008. Available at http://hal.inria.fr/inria-00288107/en/), which is written in French

New fast estimation methods stemming from control theory lead to a fresh look at time series, which bears some resemblance to "technical analysis". The results are applied to a typical object of financial engineering, namely the forecast of foreign exchange rates, via a "model-free" setting, i.e., via repeated identifications of low order linear difference equations on sliding short time windows. Several convincing computer simulations, including the prediction of the position and of the volatility with respect to the forecasted trendline, are provided. $\mathcal{Z}$-transform and differential algebra are the main mathematical tools.

Non-linear state estimation and some related topics, like parametric estimation, fault diagnosis, and perturbation attenuation, are tackled here via a new methodology in numerical differentiation. The corresponding basic system theoretic definitions and properties are presented within the framework of differential algebra, which permits to handle system variables and their derivatives of any order. Several academic examples and their computer simulations, with on-line estimations, are illustrating our viewpoint.

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.

Thanks to the nonstandard formalization of fast oscillating functions, due to P. Cartier and Y. Perrin, an appropriate mathematical framework is derived for new non-asymptotic estimation techniques, which do not necessitate any statistical analysis of the noises corrupting any sensor. Various applications are deduced for multiplicative noises, for the length of the parametric estimation windows, and for burst errors.