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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

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., Comment: 8th Joint IFAC Conference: SSSC-TDS-LPV, September 27-30, 2022 -- Montreal, Canada

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

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 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

Controlling microalgae cultivation, i.e., a crucial industrial topic today, is a challenging task since the corresponding modeling is complex, highly uncertain and time-varying. A model-free control setting is therefore introduced in order to ensure a high growth of microalgae in a continuous closed photobioreactor. Computer simulations are displayed in order to compare this design to an input-output feedback linearizing control strategy, which is widely used in the academic literature on photobioreactors. They assess the superiority of the model-free standpoint both in terms of performances and implementation simplicity., Comment: The 24th Mediterranean Conference on Control and Automation (MED'16), Athens, Greece (June 21-24, 2016)