H. Aboua¨?ssaaboua¨?ssa, M. Fliess, V. Iordanova, and C. Join, Freeway ramp metering control made easy and efficient', in 13 th IFAC Symp, Control Transportation Systems, 2012.

S. Andary, A. Chemori, M. Benoit, and J. Sallantin, A dual modelfree control of underactuated mechanical systems ? Application to the inertia wheel inverted pendulum with real-time experiments, Amer. Control Conf, 2012.

B. Andréa-novel, C. Boussard, M. Fliess, O. Hamzaoui, H. Mounier et al., Commande sans modèle de vitesse longitudinale d'un véhiculé electrique', in 6 e Conf. Internat. Francoph. Automatique, Nancy Available at http://hal.archives-ouvertes.fr/inria-00463865A mathematical explanation via " intelligent " PID controllers of the strange ubiquity of PIDs, 18 th Medit. Conf. Control Automat, 2010.

?. Aström, K. J. , H. , T. , K. J. Hang et al., Towards intelligent PID control, Advanced PID Control, Instrument Soc. Amer.. 30Åström 30Åström, pp.1-9, 1992.
DOI : 10.1016/0005-1098(92)90002-W

?. Aström, K. J. , M. , and R. M. , Feedback Systems: An Introduction for Scientists and Engineers, 2008.

J. F. Barrett, The Use of Functionals in the Analysis of Non-linear Physical Systems???, Journal of Electronics and Control, vol.253, issue.6, pp.567-615, 1963.
DOI : 10.1007/BF02546511

B. Kadri and M. , Model Free Adaptive Fuzzy Control: Beginners Approach, 2009.

A. Chambert-loir, Algèbre corporelle, ´ EditionsÉcoleEditions´EditionsÉcole Polytechnique A Field Guide to Algebra, English translation, 2005.

Y. Chang, B. Gao, and K. Gu, A Model-Free Adaptive Control to a Blood Pump Based on Heart Rate, ASAIO Journal, vol.57, issue.4, pp.262-267, 2011.
DOI : 10.1097/MAT.0b013e31821798aa

P. H. Chang, J. , and P. H. , A Systematic Method for Gain Selection of Robust PID Control for Nonlinear Plants of Second-Order Controller Canonical Form, IEEE Transactions on Control Systems Technology, vol.17, issue.2, pp.473-483, 2009.
DOI : 10.1109/TCST.2008.2000989

S. Choi, B. Andréa-novel, M. Fliess, H. Mounier, and J. Villagra, Model-free control of automotive engine and brake for Stopand-Go scenarios, 10 th Europ. Control Conf, 2009.

J. Coron and E. Trélat, Global Steady-State Controllability of One-Dimensional Semilinear Heat Equations, SIAM Journal on Control and Optimization, vol.43, issue.2, pp.549-569, 2004.
DOI : 10.1137/S036301290342471X

E. Delaleau, Algèbre différentielle, Mathématiques pour les systèmes dynamiques, pp.245-268, 2002.

J. De-miras, S. Riachy, M. Fliess, C. Join, and S. Bonnet, Vers une commande sans modèle d'un palier magnétique', in 7 e Conf, 2012.

M. G. Fliess, S. K. Marchesini, and . Mitter, Un Outil Algebrique: Les Series Formelles Non Commutatives, Mathematical System Theory, Lect. Notes Econom. Math. Syst, vol.131, pp.122-148, 1976.
DOI : 10.1007/978-3-642-48895-5_9

M. Fliess, Fonctionnelles causales non lin??aires et ind??termin??es non commutatives, Bulletin de la Société mathématique de France, vol.79, pp.3-40, 1981.
DOI : 10.24033/bsmf.1931

M. Fliess, Analyse non standard du bruit, Comptes Rendus Mathematique, vol.342, issue.10, pp.797-802, 2006.
DOI : 10.1016/j.crma.2006.02.037

URL : https://hal.archives-ouvertes.fr/inria-00001134

M. Fliess and C. Join, Intelligent PID controllers, 2008 16th Mediterranean Conference on Control and Automation, 2008.
DOI : 10.1109/MED.2008.4601995

URL : https://hal.archives-ouvertes.fr/inria-00273279

M. Fliess and C. Join, Commande sans modèle et commandè a modèle restreint', e-STA, 5 (n ? 4): 1?23, 2008.

M. Fliess and C. Join, MODEL-FREE CONTROL AND INTELLIGENT PID CONTROLLERS: TOWARDS A POSSIBLE TRIVIALIZATION OF NONLINEAR CONTROL?, 15 th IFAC Symp. System Identif., Saint-Malo, 2009.
DOI : 10.3182/20090706-3-FR-2004.00256

URL : https://hal.archives-ouvertes.fr/inria-00372325

M. Fliess, C. Join, and M. Mboup, Algebraic change-point detection, Applicable Algebra in Engineering, Communication and Computing, vol.83, issue.2, pp.131-143, 2010.
DOI : 10.1007/s00200-010-0119-z

URL : https://hal.archives-ouvertes.fr/inria-00439226

M. Fliess, C. Join, M. Mboup, and H. Sira-ramírez, Vers une commande multivariable sans modèle, 4 e Conf. Int. Francoph. Automatique, 2006.

M. Fliess, C. Join, R. , and S. , Revisiting some practical issues in the implementation of model-free control, 18 th IFAC World Congress, 2011.
DOI : 10.3182/20110828-6-IT-1002.00520

URL : https://hal.archives-ouvertes.fr/hal-00576955

M. Fliess, C. Join, R. , and S. , Rien de plus utile qu'une bonne théorie: la commande sans modèle, Journées Nationales/Journées Doctorales Modélisation Analyse Conduite Systèmes, 2011.

M. Fliess, C. Join, and H. Sira-ramírez, Robust residual generation for linear fault diagnosis: an algebraic setting with examples, International Journal of Control, vol.34, issue.14, pp.1223-1242, 2004.
DOI : 10.1080/002071704200024374

M. Fliess, C. Join, and H. Sira-ramírez, COMPLEX CONTINUOUS NONLINEAR SYSTEMS: THEIR BLACK BOX IDENTIFICATION AND THEIR CONTROL, 14 th Symp, 2006.
DOI : 10.3182/20060329-3-AU-2901.00062

URL : https://hal.archives-ouvertes.fr/inria-00000824

M. Fliess, C. Join, and H. Sira-ramírez, Non-linear estimation is easy, International Journal of Modelling, Identification and Control, vol.4, issue.1, pp.12-27, 2008.
DOI : 10.1504/IJMIC.2008.020996

URL : https://hal.archives-ouvertes.fr/inria-00158855

M. Fliess, J. Lévine, P. Martin, and P. And-rouchon, Flatness and defect of non-linear systems: introductory theory and examples, International Journal of Control, vol.4, issue.6, pp.61-1327, 1995.
DOI : 10.1109/9.73561

M. Fliess and R. Marquez, Continuous-time linear predictive control and flatness: A module-theoretic setting with examples, International Journal of Control, vol.73, issue.7, pp.606-623, 2002.
DOI : 10.1080/002071700219452

M. Fliess, R. Marquez, E. Delaleau, and H. Sira-ramírez, Correcteurs proportionnels-intégraux généralisés', ESAIM Control Optimiz, Calc. Variat, vol.7, pp.23-41, 2002.

M. Fliess and H. Sira-ramírez, An algebraic framework for linear identification', ESAIM Control Optimiz, Calc. Variat, vol.9, pp.151-168, 2003.

M. Fliess and H. Sira-ramírez, Closed-loop parametric identification for continuous-time linear systems via new algebraic techniques Identification of Continuous-time Models from Sampled Data, pp.362-391, 2008.

M. Fliess, H. Sira-ramírez, and R. Marquez, Regulation of nonminimum phase outputs: a flatness based approach, Perspectives in Control ?Theory and Applications: a Tribute to Ioan Doré Landau, pp.143-164, 1998.

S. Formentin, P. De-filippi, M. Corno, M. Tanelli, and S. Savaresi, Data-Driven Design of Braking Control Systems, IEEE Transactions on Control Systems Technology, vol.21, issue.1, pp.186-193, 2013.
DOI : 10.1109/TCST.2011.2171965

S. Formentin, P. De-filippi, M. Tanelli, and S. Savaresi, Model-free control for active braking systems in sport motorcycles *, th IFAC Symp. Nonlinear Control Systems, 2010.
DOI : 10.3182/20100901-3-IT-2016.00094

P. Gédouin, E. Delaleau, J. Bourgeot, C. Join, S. Arab-chirani et al., Experimental comparison of classical PID and model-free control: Position control of a shape memory alloy active spring, Control Engineering Practice, vol.19, issue.5, pp.433-441, 2011.
DOI : 10.1016/j.conengprac.2011.01.005

N. Gehring, T. Knüppel, J. Rudolph, and F. Woittennek, Algebraische Methoden zur Parameteridentifikation für das schwere Seil, pp.514-521, 2012.
DOI : 10.1524/auto.2012.1026

B. Hahn and K. R. Oldham, A Model-Free ON–OFF Iterative Adaptive Controller Based on Stochastic Approximation, IEEE Transactions on Control Systems Technology, vol.20, issue.1, pp.196-204, 2012.
DOI : 10.1109/TCST.2011.2104360

J. Han, From PID to Active Disturbance Rejection Control, IEEE Transactions on Industrial Electronics, vol.56, issue.3, pp.900-906, 2009.
DOI : 10.1109/TIE.2008.2011621

L. Hong-wei, C. Rong-min, H. , and Z. , Application research on model-free control strategy of Permanent Magnetism Linear Synchronous Motors, 2011 International Conference on Electrical Machines and Systems, 2011.
DOI : 10.1109/ICEMS.2011.6073683

C. Join, J. Masse, and M. Fliess, Etude pr??liminaire d'une commande sans mod??le pour papillon de moteur, Journal Europ??en des Syst??mes Automatis??s, vol.42, issue.2-3, pp.337-354, 2008.
DOI : 10.3166/jesa.42.337-354

C. Join, G. Robert, and M. Fliess, Model-free based water level control for hydroelectric power plants', in IFAC Conf. Control Method. Technologies Energy Efficiency, Vilamoura, 2010.

C. Join, G. Robert, and M. Fliess, Vers une commande sans modèle pour aménagements hydroélectriques en cascade', in 6 e Conf, Internat. Francoph. Automat, 2010.

L. H. Keel and S. P. Bhattacharyya, Controller Synthesis Free of Analytical Models: Three Term Controllers, IEEE Transactions on Automatic Control, vol.53, issue.6, pp.1353-1369, 2008.
DOI : 10.1109/TAC.2008.925810

N. J. Killingsworth and M. Krstic, PID tuning using extremum seeking: online, model-free performance optimization, IEEE Control Systems Magazine, vol.26, issue.1, pp.70-79, 2006.
DOI : 10.1109/MCS.2006.1580155

E. R. Kolchin, Differential Algebra and Algebraic Groups, 1973.

F. Lafont, N. Pessel, J. Balmat, and M. Fliess, On the model-free control of an experimental greenhouse, Int. Conf. Modeling Simulation Control, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00831598

F. Lamnabhi-lagarrigue, Volterra and Fliess series expansions for nonlinear systems The Control Handbook, pp.879-888, 1995.

M. Lerch, Sur un point de la théorie des fonctions génératrices d'Abel', Acta Math, pp.339-352, 1903.

J. Lévine, Analysis and Control of Nonlinear Systems ? A flatness-based approach, 2009.

D. Y. Liu, O. Gibaru, and W. Perruquetti, Error analysis of Jacobi derivative estimators for noisy signals, Numerical Algorithms, vol.21, issue.12, pp.53-83, 2011.
DOI : 10.1007/s11075-011-9447-8

URL : https://hal.archives-ouvertes.fr/inria-00573270

C. Lobry and T. Sari, Non-standard analysis and representation of reality, International Journal of Control, vol.1249, issue.3, pp.519-536, 2008.
DOI : 10.1007/978-3-211-49905-4

E. Malis and F. Chaumette, Theoretical improvements in the stability analysis of a new class of model-free visual servoing methods, IEEE Transactions on Robotics and Automation, vol.18, issue.2, pp.176-186, 2002.
DOI : 10.1109/TRA.2002.999646

URL : https://hal.archives-ouvertes.fr/inria-00352094

M. Mboup, C. Join, and M. Fliess, Numerical differentiation with annihilators in noisy environment, Numerical Algorithms, vol.14, issue.12, pp.439-467, 2009.
DOI : 10.1007/s11075-008-9236-1

URL : https://hal.archives-ouvertes.fr/inria-00319240

L. Menhour, B. Andréa-novel, C. Boussard, M. Fliess, and H. Mounier, Algebraic nonlinear estimation and flatness-based lateral/longitudinal control for automotive vehicles, 2011 14th International IEEE Conference on Intelligent Transportation Systems (ITSC), 2011.
DOI : 10.1109/ITSC.2011.6083044

URL : https://hal.archives-ouvertes.fr/hal-00611950

L. Michel, C. Join, M. Fliess, P. Sicard, and A. Chériti, Model-free control of dc/dc converters, 2010 IEEE 12th Workshop on Control and Modeling for Power Electronics (COMPEL), 2010.
DOI : 10.1109/COMPEL.2010.5562385

URL : https://hal.archives-ouvertes.fr/inria-00495776

V. Milanes, J. Villagra, J. Perez, and C. Gonzalez, Low-Speed Longitudinal Controllers for Mass-Produced Cars: A Comparative Study, IEEE Transactions on Industrial Electronics, vol.59, issue.1, pp.620-628, 2012.
DOI : 10.1109/TIE.2011.2148673

URL : https://hal.archives-ouvertes.fr/hal-00732892

R. Morales, V. Feliu, H. Sira-ramírez, and H. , Nonlinear Control for Magnetic Levitation Systems Based on Fast Online Algebraic Identification of the Input Gain, IEEE Transactions on Control Systems Technology, vol.19, issue.4, pp.757-771, 2011.
DOI : 10.1109/TCST.2010.2057511

A. Morales, A. Nieto, J. R. Trapero, J. Chicharro, and P. Pintado, An adaptive pneumatic suspension based on the estimation of the excitation frequency, J. Sound Vibration, vol.330, pp.1891-1903, 2011.

R. Morales and H. Sira-ramírez, Trajectory tracking for the magnetic ball levitation system via exact feedforward linearisation and GPI control, International Journal of Control, vol.2, issue.6, pp.1155-1166, 2010.
DOI : 10.1080/00207170210156189

M. Ali, A. Join, C. Hamelin, and F. , Fault diagnosis without a priori model, Systems Control Lett, vol.61, pp.316-321, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00650811

O. Dwyer and A. , Handbook of PI and PID Controller Tuning Rules, 2009.

H. Olsson, K. J. Aström, C. Canudas-de-wit, M. Gäfvert, and P. Lischinsky, Friction Models and Friction Compensation, European Journal of Control, vol.4, issue.3, pp.176-195, 1998.
DOI : 10.1016/S0947-3580(98)70113-X

E. Pereira, J. R. Trapero, I. Muñoz, and V. Feliu, Adaptive input shaping for maneuvering flexible structures using an algebraic identification technique, Automatica, pp.45-1046, 2009.

E. Pereira, J. R. Trapero, I. Muñoz, and V. Feliu, Algebraic identification of the first two natural frequencies of flexible-beam-like structures, Mechanical Systems and Signal Processing, vol.25, issue.7, pp.2324-2335, 2011.
DOI : 10.1016/j.ymssp.2011.03.007

S. Riachy, M. Fliess, and C. Join, High-order sliding modes and intelligent PID controllers: First steps toward a practical comparison, 18 th IFAC World Congress, 2011.
DOI : 10.3182/20110828-6-IT-1002.01472

URL : https://hal.archives-ouvertes.fr/hal-00580970

S. Riachy, M. Fliess, C. Join, and J. Barbot, Vers une simplification de la commande non linéaire: l'exemple d'un avionàavionà décollage vertical, 6 e Conf. Internat. Francoph. Automatique, 2010.

S. Coelho, L. , W. Pessôa, M. Rodrigues-sumar, R. et al., Model-free adaptive control design using evolutionary-neural compensator', Expert Systems Appl, pp.499-508, 2010.

H. Sira-ramírez, SLIDING MODES, ??-MODULATORS, AND GENERALIZED PROPORTIONAL INTEGRAL CONTROL OF LINEAR SYSTEMS, Asian Journal of Control, vol.7, issue.2, pp.467-475, 2003.
DOI : 10.1111/j.1934-6093.2003.tb00164.x

F. Sorcia-vázquez, C. García-beltrán, J. Reyes-reyes, A. Rodríguez-palacios, and A. , Control de un brazo robot de eslabón flexible mediante PID generalizado y control sin modelo, Congr, 2010.

J. C. Spall and J. A. And-cristion, Model-free control of nonlinear stochastic systems with discrete-time measurements, IEEE Transactions on Automatic Control, vol.43, issue.9, pp.1198-1210, 1998.
DOI : 10.1109/9.718605

J. Swevers, C. Lauwerys, B. Vandersmissen, M. Maes, K. Reybrouck et al., A model-free control structure for the on-line tuning of the semi-active suspension of a passenger car, Mechanical Systems Signal Processing, pp.1422-1436, 2007.
DOI : 10.1016/j.ymssp.2006.05.005

H. J. Sussmann, Semigroup Representations, Bilinear Approximation of Input-Output Maps, and Generalized Inputs, Mathematical System Theory, Lect. Notes Econom. Math. Syst, vol.131, pp.172-191, 1976.
DOI : 10.1007/978-3-642-48895-5_12

S. Syafiie, F. Tadeo, E. Martinez, and T. Alvarez, Model-free control based on reinforcement learning for a wastewater treatment problem, Applied Soft Computing, vol.11, issue.1, pp.73-82, 2011.
DOI : 10.1016/j.asoc.2009.10.018

J. R. Trapero, H. Sira-ramírez, and V. F. Battle, An algebraic frequency estimator for a biased and noisy sinusoidal signal, Signal Processing, pp.1188-1201, 2007.
DOI : 10.1016/j.sigpro.2006.10.006

J. R. Trapero, H. Sira-ramírez, and V. F. Battle, A fast on-line frequency estimator of lightly damped vibrations in flexible structures, Journal of Sound and Vibration, vol.307, issue.1-2, pp.365-378, 2007.
DOI : 10.1016/j.jsv.2007.07.005

J. R. Trapero, H. Sira-ramírez, and V. F. Battle, On the algebraic identification of the frequencies, amplitudes and phases of two sinusoidal signals from their noisy sum, International Journal of Control, vol.339, issue.3, pp.507-518, 2008.
DOI : 10.1016/j.sigpro.2004.05.008

A. Tustin, The effects of backlash and of speed-dependent friction on the stability of closed-cycle control systems, Journal of the Institution of Electrical Engineers - Part IIA: Automatic Regulators and Servo Mechanisms, vol.94, issue.1, pp.143-151, 1947.
DOI : 10.1049/ji-2a.1947.0021

J. Villagra, B. Andréa-novel, S. Choi, M. Fliess, and H. Mounier, Robust stop-and-go control strategy: an algebraic approach for non-linear estimation and control, International Journal of Vehicle Autonomous Systems, vol.7, issue.3/4, pp.270-291, 2009.
DOI : 10.1504/IJVAS.2009.033264

J. Villagra and C. Balaguer, A MODEL-FREE APPROACH FOR ACCURATE JOINT MOTION CONTROL IN HUMANOID LOCOMOTION, International Journal of Humanoid Robotics, vol.08, issue.01, pp.27-46, 2011.
DOI : 10.1142/S0219843611002332

J. Villagra and D. Herrero-pérez, A Comparison of Control Techniques for Robust Docking Maneuvers of an AGV, IEEE Transactions on Control Systems Technology, vol.20, issue.4, pp.1116-1123, 2012.
DOI : 10.1109/TCST.2011.2159794

J. Villagra, V. Milanés, J. Pérez, and T. De-pedro, Control basado en PID inteligentes: aplicaci??n al control de crucero de un veh??culo a bajas velocidades, Revista Iberoamericana de Autom??tica e Inform??tica Industrial RIAI, vol.7, issue.4, pp.44-52, 2010.
DOI : 10.1016/S1697-7912(10)70059-5

V. Volterra, Theory of Functionals and of Integral and Integro- Differential Equations, 1930.

J. Wang, H. Mounier, A. Cela, and S. Niculescu, Event driven intelligent PID controllers with applications to motion control, 18 th IFAC World Congress, 2011.
DOI : 10.3182/20110828-6-IT-1002.02960

URL : https://hal.archives-ouvertes.fr/hal-00832014

P. Xu, G. Li, W. , and K. , Self Tuning of PID Controller Based on Simultaneous Perturbation Stochastic Approximation, Advances Electronic Engineering Communication Management, pp.647-652, 2012.
DOI : 10.1007/978-3-642-27287-5_105

K. Youcef-toumi and O. Ito, A Time Delay Controller for Systems With Unknown Dynamics, Journal of Dynamic Systems, Measurement, and Control, vol.112, issue.1, pp.133-142, 1990.
DOI : 10.1115/1.2894130

Q. Zheng, Z. Chen, and Z. Gao, A practical approach to disturbance decoupling control, Control Engineering Practice, vol.17, issue.9, pp.1016-1025, 2009.
DOI : 10.1016/j.conengprac.2009.03.005