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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