T. Model-with, 20 4.2.1 Impact of thermal variables on the cost function, p.20

A. Agrachev and Y. Sachkov, Control theory from the geometric view-point, 2004.

D. Ambühl, O. Sundström, A. Sciarretta, and L. Guzzella, Explicit optimal control policy and its practical application for hybrid electric powertrains, Control Engineering Practice, vol.18, issue.12, pp.1429-1439, 2010.
DOI : 10.1016/j.conengprac.2010.08.003

G. Andrews, J. Harris, and A. Ounzain, SI Engine Warm-Up: Water and Lubricating Oil Temperature Influences, SAE Technical Paper Series, 1989.
DOI : 10.4271/892103

M. Gaïd, G. Corde, A. Chasse, and B. Léty, Heterogeneous model integration and virtual experimentation using xmod: application to hybrid powertrain design and validation, 2010.

A. B. Khaled, Distributed real-time simulation of numerical models: application to powertrain, 2014.
URL : https://hal.archives-ouvertes.fr/tel-01144469

A. Bensoussan, Perturbation methods in optimal control, 1988.

G. Bertotti, A. Boglietti, M. Chiampi, D. Chiarabaglio, F. Fiorillo et al., An improved estimation of iron losses in rotating electrical machines, IEEE Transactions on Magnetics, vol.27, issue.6, pp.5007-5009, 1991.
DOI : 10.1109/20.278722

D. Bertsekas, Dynamic programming and optimal control, Athena Scientific, 2012.

A. Bonfils, Experimental closed-loop control of SCR aftertreatment systems using NOx sensors cross-sensitive to NH3, 2013.
URL : https://hal.archives-ouvertes.fr/tel-01139394

J. Bonnans, . Th, and . Guilbaud, Using logarithmic penalties in the shooting algorithm for optimal control problems, Optimal Control Applications and Methods, vol.9, issue.5, 2001.
DOI : 10.1002/oca.730
URL : https://hal.archives-ouvertes.fr/inria-00072350

J. Bonnans and A. Hermant, Stability and sensitivity analysis for optimal control problems with a first-order state constraint and application to continuation methods, ESAIM: Control, Optimisation and Calculus of Variations, vol.14, issue.4, pp.825-863, 2008.
DOI : 10.1051/cocv:2008016

H. Borhan, A. Vahidi, A. Phillips, and M. Kuang, Predictive energy management of a power-split hybrid electric vehicle, 2009 American Control Conference, pp.3970-3976, 2009.
DOI : 10.1109/ACC.2009.5160451

A. Bryson and Y. Ho, Applied optimal control, 1969.

A. Chasse, G. Corde, A. Mastro, and F. Perez, Hyhil: online optimal control of a parallel hybrid with after treatment constraint integration, Proc. of IEEE Vehicle Power and Propulsion Conference, pp.1-6, 2010.

A. Chasse, P. Pognant-gros, and A. Sciarretta, Online Implementation of an Optimal Supervisory Control for a Parallel Hybrid Powertrain, SAE International Journal of Engines, vol.2, issue.1, pp.1630-1638, 2009.
DOI : 10.4271/2009-01-1868

A. Chasse and A. Sciarretta, Supervisory control of hybrid powertrains: An experimental benchmark of offline optimization and online energy management, Control Engineering Practice, vol.19, issue.11, pp.1253-1265, 2011.
DOI : 10.1016/j.conengprac.2011.04.008

J. Chen and M. Salman, Learning energy management strategy for hybrid electric vehicles, Proc. of IEEE Vehicle Power and Propulsion Conference, pp.68-73, 2005.

B. De-jager, T. Van-keulen, and J. Kessels, Optimal control of hybrid vehicles
DOI : 10.1007/978-1-4471-5076-3

S. Delprat, T. Guerra, and J. Rimaux, Control strategies for hybrid vehicles: synthesis and evaluation, 2003 IEEE 58th Vehicular Technology Conference. VTC 2003-Fall (IEEE Cat. No.03CH37484), pp.3246-3250, 2003.
DOI : 10.1109/VETECF.2003.1286250

S. Delprat and T. Hofman, Hybrid Vehicle Optimal Control: Linear Interpolation and Singular Control, 2014 IEEE Vehicle Power and Propulsion Conference (VPPC), pp.1-6, 2014.
DOI : 10.1109/VPPC.2014.7007080

W. Dib, A. Chasse, P. Moulin, A. Sciarretta, and G. Corde, Optimal energy management for an electric vehicle in eco-driving applications, Control Engineering Practice, vol.29, pp.299-307, 2014.
DOI : 10.1016/j.conengprac.2014.01.005
URL : https://hal.archives-ouvertes.fr/hal-01100439

A. Dontchev, Introduction, Lecture Notes in Control and Information Sciences, vol.52, pp.1-153, 1983.
DOI : 10.1007/BFb0043613

R. Dutta, L. Chong, and F. Rahman, ANALYSIS AND EXPERIMENTAL VERIFICATION OF LOSSES IN A CONCENTRATED WOUND INTERIOR PERMANENT MAGNET MACHINE, Progress In Electromagnetics Research B, vol.48, pp.221-248, 2013.
DOI : 10.2528/PIERB12110715

L. Eriksson, Mean value models for exhaust system temperatures. SAE Technical Paper, 2002.

L. Eriksson and L. Nielsen, Modeling and control of engines and drivelines, 2014.
DOI : 10.1002/9781118536186

A. Fiacco and G. Mccormick, Nonlinear programming: sequential unconstrained minimization techniques, 1968.
DOI : 10.1137/1.9781611971316

J. Gao, G. Zhu, E. Strangas, and F. Sun, Equivalent fuel consumption optimal control of a series hybrid electric vehicle, Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, vol.110, issue.8, pp.1003-1018, 2009.
DOI : 10.1243/09544070JAUTO1074

Y. Gaoua, S. Caux, P. Lopez, and J. Salvany, On-line HEV energy management using a fuzzy logic, 2013 12th International Conference on Environment and Electrical Engineering, pp.46-51, 2013.
DOI : 10.1109/EEEIC.2013.6549587
URL : https://hal.archives-ouvertes.fr/hal-00814204

K. Graichen, Feedforward control design for finite time transition problems of nonlinear systems with input and output constraints, 2006.

K. Graichen, A. Kugi, N. Petit, and F. Chaplais, Handling constraints in optimal control with saturation functions and system extension, Systems & Control Letters, vol.59, issue.11, pp.671-679, 2010.
DOI : 10.1016/j.sysconle.2010.08.003
URL : https://hal.archives-ouvertes.fr/hal-00553051

K. Graichen and N. Petit, Constructive Methods for Initialization and Handling Mixed State-Input Constraints in Optimal Control, Journal of Guidance, Control, and Dynamics, vol.31, issue.5, pp.1334-1343, 2008.
DOI : 10.2514/1.33870
URL : https://hal.archives-ouvertes.fr/hal-00447826

L. Guzzella and A. Sciarretta, Vehicle propulsion systems, 2013.
DOI : 10.1007/978-3-642-35913-2

C. Hargraves and S. Paris, Direct trajectory optimization using nonlinear programming and collocation, Journal of Guidance, Control, and Dynamics, vol.10, issue.4, pp.338-342, 1987.
DOI : 10.2514/3.20223

N. Karmarkar, A new polynomial-time algorithm for linear programming, Combinatorica, vol.244, issue.S, pp.373-395, 2008.
DOI : 10.1007/BF02579150

S. Kermani, S. Delprat, R. Trigui, and T. Guerra, Predictive energy management for hybrid vehicle, Control Engineering Practice, vol.20, issue.4, pp.408-420, 2012.
DOI : 10.1016/j.conengprac.2011.12.001
URL : https://hal.archives-ouvertes.fr/hal-00877628

J. Kessels, M. Koot, P. Van-den, D. Bosch, and . Kok, Online Energy Management for Hybrid Electric Vehicles, IEEE Transactions on Vehicular Technology, vol.57, issue.6, pp.3428-3440, 2008.
DOI : 10.1109/TVT.2008.919988

H. Khalil, Nonlinear systems, 2002.

U. Kiencke and L. Nielsen, Automotive control systems: for engine, driveline, and vehicle, 2005.

N. Kim, S. Cha, and H. Peng, Optimal control of hybrid electric vehicles based on Pontryagin's minimum principle, IEEE Transactions on Control Systems Technology, vol.19, pp.1279-1287, 2011.

I. K. Yoo, K. Simpson, M. Bell, and S. Majkowski, An Engine Coolant Temperature Model and Application for Cooling System Diagnosis, SAE Technical Paper Series, 2000.
DOI : 10.4271/2000-01-0939

O. Lepreux, Model-based temperature control of a diesel oxidation catalyst, Journal of Process Control, vol.22, issue.1, 2009.
DOI : 10.1016/j.jprocont.2011.10.012
URL : https://hal.archives-ouvertes.fr/hal-00661530

J. Lescot, A. Sciarretta, Y. Chamaillard, and A. Charlet, On the integration of optimal energy management and thermal management of hybrid electric vehicles, 2010 IEEE Vehicle Power and Propulsion Conference, 2010.
DOI : 10.1109/VPPC.2010.5729158

C. Lin, H. Peng, J. Grizzle, and J. Kang, Power management strategy for a parallel hybrid electric truck, IEEE Transactions on Control Systems Technology, vol.11, pp.839-849, 2003.

D. Maamria, F. Chaplais, N. Petit, and A. Sciarretta, Numerical optimal control as a method to evaluate the benefit of thermal management in hybrid electric vehicles, Proc. of the IFAC World Congress, pp.4807-4812, 2014.
DOI : 10.3182/20140824-6-ZA-1003.00901

D. Maamria, F. Chaplais, N. Petit, and A. Sciarretta, On the impact of model simplification in input constrained optimal control: Application to HEV energy-thermal management, 53rd IEEE Conference on Decision and Control, pp.2529-2535, 2014.
DOI : 10.1109/CDC.2014.7039775

P. Malisani, Dynamic control of energy in buildings using constrained optimal control by interior penalty, 2012.
URL : https://hal.archives-ouvertes.fr/pastel-00740044

P. Malisani, F. Chaplais, and N. Petit, Design of penalty functions for optimal control of linear dynamical systems under state and input constraints, IEEE Conference on Decision and Control and European Control Conference, pp.6697-6704, 2011.
DOI : 10.1109/CDC.2011.6160718
URL : https://hal.archives-ouvertes.fr/hal-00676305

P. Malisani, F. Chaplais, and N. Petit, A constructive interior penalty method for non linear optimal control problems with state and input constraints, Proc. of the American Control Conference, pp.2669-2676, 2012.

P. Malisani, F. Chaplais, and N. Petit, An interior penalty method for optimal control problems with state and input constraints of non-linear systems, Optimal Control, p.2014
URL : https://hal.archives-ouvertes.fr/hal-01111710

N. Marc, E. Prada, A. Sciarretta, S. Anwer, F. Vangraefschepe et al., Sizing and fuel consumption evaluation methodology for hybrid light duty vehicles, Hybrid and Fuel Cell Electric Vehicle Symposium & Exhibition, pp.249-258, 2010.

C. Martínez, Energy efficiency in the automotive industry evidence from germany and colombia. Environment, Development and Sustainability, pp.367-383, 2011.

A. Mastro, A. Chasse, P. Pognant-gros, and G. Corde, Advanced Hybrid Vehicle Simulation: from ???Virtual??? to ???HyHiL??? test bench, SAE Technical Paper Series, 2009.
DOI : 10.4271/2009-24-0068

F. Mensing, E. Bideaux, R. Trigui, J. Ribet, and B. Jeanneret, Eco-driving: an economic or ecologic driving style? Transportation Research Part C: Emerging Technologies, pp.110-121, 2014.

F. Merz, A. Sciarretta, J. Dabadie, and L. Serrao, On the Optimal Thermal Management of Hybrid-Electric Vehicles with Heat Recovery Systems, Oil & Gas Science and Technology ??? Revue d???IFP Energies nouvelles, vol.67, issue.4, pp.601-612, 2012.
DOI : 10.2516/ogst/2012017
URL : https://hal.archives-ouvertes.fr/hal-00784720

P. Michel, A. Charlet, G. Colin, Y. Chamaillard, C. Nouillant et al., Energy management of HEV to optimize fuel consumption and pollutant emissions, Proc. of International Symposium on Advanced Vehicule Control, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00731458

P. Michel, A. Charlet, G. Colin, Y. Chamaillard, C. Nouillant et al., 3 WCC temperature integration in a gasoline-HEV optimal energy management strategy Advances in Mechanical Engineering, 2014.

P. Michel, A. Charlet, G. Colin, Y. Chamaillard, C. Nouillant et al., Catalytic converter modeling for optimal gasoline-HEV energy management, Proc. of the IFAC World Congress, pp.6636-6641, 2014.
DOI : 10.3182/20140824-6-ZA-1003.01419
URL : https://hal.archives-ouvertes.fr/hal-01062316

T. Morel and R. Keribar, Warm-up characteristics of a spark ignition engine as a function of speed and load. SAE Technical Paper, 1990.

C. Musardo, G. Rizzoni, and B. Staccia, A-ECMS: an adaptive algorithm for hybrid electric vehicle energy management, 44th IEEE Conference on Decision and Control, and the European Control Conference, pp.1816-1823, 2005.

S. Oh and A. Hildreth, Estimating the Technical Improvement of Energy Efficiency in the Automotive Industry???Stochastic and Deterministic Frontier Benchmarking Approaches, Energies, vol.7, issue.9, pp.6196-6222, 2014.
DOI : 10.3390/en7096196

S. Onori and L. Serrao, On adaptive-ECMS strategies for hybrid electric vehicles, Proc. of the International Scientific Conference on Hybrid and Electric Vehicles, pp.1-7, 2011.

T. Padovani, M. Debert, G. Colin, and Y. Chamaillard, Optimal energy management strategyincluding battery health through thermal management for hybrid vehicles, IFAC Symposium on Advances in Automotive Control, pp.384-389, 2013.

G. Paganelli, S. Delprat, T. Guerra, J. Rimaux, and J. Santin, Equivalent consumption minimization strategy for parallel hybrid powertrains, Vehicular Technology Conference. IEEE 55th Vehicular Technology Conference. VTC Spring 2002 (Cat. No.02CH37367), pp.2076-2081, 2002.
DOI : 10.1109/VTC.2002.1002989

G. Paganelli, G. Ercole, A. Brahma, Y. Guezennec, and G. Rizzoni, General supervisory control policy for the energy optimization of charge-sustaining hybrid electric vehicles, JSAE Review, vol.22, issue.4, pp.511-518, 2001.
DOI : 10.1016/S0389-4304(01)00138-2

E. Philipp, Noncausal and causal optimization strategies for hybrid electric vehicles, 2014.

L. Pontryagin, V. Boltyanskii, R. Gamkrelidze, and E. Mishchenko, The mathematical theory of optimal processes, 1962.

S. Roberts and J. Shipman, Continuation in shooting methods for two-point boundary value problems, Journal of Mathematical Analysis and Applications, vol.18, issue.1, 1972.
DOI : 10.1016/0022-247X(67)90181-3

G. Rousseau, D. Sinoquet, and P. Rouchon, Constrained Optimization of Energy Management for a Mild-Hybrid Vehicle, Oil & Gas Science and Technology - Revue de l'IFP, vol.62, issue.4, pp.623-634, 2007.
DOI : 10.2516/ogst:2007056

G. Rousseau, D. Sinoquet, A. Sciarretta, and Y. Milhau, Design optimisation and optimal control for hybrid vehicles, Proc. of International Conference on Engineering Optimization, 2008.

S. Ebbesen, Optimal sizing and control of hybrid electric vehicles, 2012.

A. Sciarretta, M. Back, and L. Guzzella, Optimal Control of Parallel Hybrid Electric Vehicles, IEEE Transactions on Control Systems Technology, vol.12, issue.3, pp.352-363, 2004.
DOI : 10.1109/TCST.2004.824312

A. Sciarretta, J. Dabadie, and G. Font, Automatic model-based generation of optimal energy management strategies for hybrid powertrains, Proc. of the SIA Powertrain Conference, 2015.

A. Sciarretta, D. Di-domenico, P. Pognant-gros, and G. Zito, Optimal energy management of automotive battery systems including thermal dynamics and ageing. Optimization and Optimal Control in Automotive Systems, 2014.

A. Sciarretta and L. Guzzella, Control of hybrid electric vehicles, IEEE Control Systems Magazine, vol.27, issue.2, pp.60-70, 2007.
DOI : 10.1109/MCS.2007.338280
URL : https://hal.archives-ouvertes.fr/hal-00832475

A. Sciarretta and N. Petit, Optimal drive of electric vehicles using an inversion-based trajectory generation approach, 18th IFAC World Congress, pp.14519-14526, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00646523

L. Serrao, S. Onori, and G. Rizzoni, ECMS as a realization of Pontryagin's minimum principle for HEV control, 2009 American Control Conference, pp.3964-3969, 2009.
DOI : 10.1109/ACC.2009.5160628

L. Serrao, S. Onori, A. Sciarretta, Y. Guezennec, and G. Rizzoni, Optimal energy management of hybrid electric vehicles including battery aging, Proceedings of the 2011 American Control Conference, pp.2125-2130, 2011.
DOI : 10.1109/ACC.2011.5991576

L. Serrao, A. Sciarretta, O. Grondin, A. Chasse, Y. Creff et al., Open Issues in Supervisory Control of Hybrid Electric Vehicles: A Unified Approach Using Optimal Control Methods, Proc. of RHEVE, Int. Scient. Conf. on Hybrid and Electric Vehicles, 2011.
DOI : 10.2516/ogst/2012080
URL : https://hal.archives-ouvertes.fr/hal-00832475

L. Shampine, J. Kierzenka, and M. Reichelt, Solving boundary value problems for ordinary differential equations in Matlab with bvp4c

P. Shayler, S. Christian, and T. Ma, A Model for the Investigation of Temperature, Heat Flow and Friction Characteristics During Engine Warm-Up, SAE Technical Paper Series, pp.667-675, 1993.
DOI : 10.4271/931153

E. Silvas, T. Hofman, and M. Steinbuch, Review of Optimal Design Strategies for Hybrid Electric Vehicles, IFAC Proceedings Volumes, vol.45, issue.30, pp.57-64, 2012.
DOI : 10.3182/20121023-3-FR-4025.00054

M. Sivertsson and L. Eriksson, Design and Evaluation of Energy Management using Map-Based ECMS for the PHEV Benchmark, Oil & Gas Science and Technology ??? Revue d???IFP Energies nouvelles, vol.70, issue.1, pp.195-211, 2014.
DOI : 10.2516/ogst/2014018

G. Tamai, T. Hoang, J. Taylor, and C. Skaggs, Saturn Engine Stop-Start System with an Automatic Transmission, SAE Technical Paper Series, 2001.
DOI : 10.4271/2001-01-0326

K. Van-berkel, W. Klemm, T. Hofman, B. Vroemen, and M. Steinbuch, Optimal energy management for a mechanical-hybrid vehicle with cold start conditions, European Control Conference, pp.452-457, 2013.

K. Van-berkel, W. Klemm, T. Hofman, B. Vroemen, and M. Steinbuch, Optimal Control of a Mechanical Hybrid Powertrain With Cold-Start Conditions, IEEE Transactions on Vehicular Technology, vol.63, issue.4, pp.1555-1566, 2014.
DOI : 10.1109/TVT.2013.2287193

A. Vasilieva and M. Dmitriev, Singular perturbations in optimal control problems, Journal of Soviet Mathematics, vol.16, issue.No. 1, pp.1579-1629, 1986.
DOI : 10.1007/BF01262406

S. Vukosavic, Electrical machines, 2012.
DOI : 10.1007/978-1-4614-0400-2

L. Yong-chen and S. Li, City bus idle stop-start system simulation analysis, 2011 International Conference on Mechatronic Science, Electric Engineering and Computer (MEC), pp.763-766, 2011.
DOI : 10.1109/MEC.2011.6025576

Y. Zhu, Y. Chen, G. Tian, H. Wu, and Q. Chen, FOUR-STEP METHOD TO DESIGN THE ENERGY MANAGEMENT STRATEGY FOR HYBRID VEHICLES, Proc. of the American Control Conference, pp.156-161, 2004.
DOI : 10.3901/JME.2004.08.127