Bibliography

Major publications by the team in recent years

• 1A. Aftalion, J. F. Bonnans.
  
  Optimization of running strategies based on anaerobic energy and variations of velocity, in: SIAM Journal of Applied Mathematics, October 2014, vol. 74, n^o 5, pp. 1615-1636.
  
  https://hal.inria.fr/hal-00851182
• 2M. S. Aronna, J. F. Bonnans, B. S. Goh.
  
  Second order analysis of state-constrained control-affine problems, in: Mathematical Programming, Series A, January 2016, vol. 160, n^o 1, pp. 115-147.
  
  https://hal.inria.fr/hal-01081111
• 3M. S. Aronna, J. F. Bonnans, A. Kröner.
  
  Optimal Control of Infinite Dimensional Bilinear Systems: Application to the Heat and Wave Equations, in: Mathematical Programming B, November 2016, 32 p.
  
  https://hal.inria.fr/hal-01273496
• 4M. S. Aronna, J. F. Bonnans, P. Martinon.
  
  A Shooting Algorithm for Optimal Control Problems with Singular Arcs, in: Journal of Optimization Theory and Applications, August 2013, vol. 158, n^o 2, pp. 419-459. [ DOI : 10.1007/s10957-012-0254-8 ]
  
  https://hal.inria.fr/inria-00631332
• 5J. F. Bonnans, X. Dupuis, L. Pfeiffer.
  
  Second-order necessary conditions in Pontryagin form for optimal control problems, in: SIAM Journal on Control and Optimization, 2014, vol. 52, n^o 6, pp. 3887-3916. [ DOI : 10.1137/130923452 ]
  
  https://hal.inria.fr/hal-00825273
• 6J. F. Bonnans, X. Tan.
  
  A model-free no-arbitrage price bound for variance options, in: Applied Mathematics and Optimization, July 2013, vol. 68, n^o 1, pp. 43-73. [ DOI : 10.1007/s00245-013-9197-1 ]
  
  https://hal.inria.fr/inria-00634387
• 7B. Bonnard, M. Claeys, O. Cots, P. Martinon.
  
  Geometric and numerical methods in the contrast imaging problem in nuclear magnetic resonance, in: Acta Applicandae Mathematicae, February 2015, vol. 135, n^o 1, pp. 5-45. [ DOI : 10.1007/s10440-014-9947-3 ]
  
  https://hal.inria.fr/hal-00867753
• 8L. Giraldi, P. Martinon, M. Zoppello.
  
  Optimal Design for Purcell Three-link Swimmer, in: Physical Review, February 2015, vol. 91, n^o 2, 023012.
  
  https://hal.archives-ouvertes.fr/hal-01098501
• 9A. Kröner, K. Kunisch, B. Vexler.
  
  Semismooth Newton methods for optimal control of the wave equation with control constraints, in: SIAM Journal on Control and Optimization, 2011, vol. 49, n^o 2, pp. 830–858.
  
  http://dx.doi.org/10.1137/090766541
• 10A. Kröner, K. Kunisch, H. Zidani.
  
  Optimal feedback control of undamped wave equations by solving a HJB equation, in: ESAIM: Control, Optimisation and Calculus of Variations, 2014, vol. 21, n^o 2, pp. 442 - 464. [ DOI : 10.1051/cocv/2014033 ]
  
  https://hal.archives-ouvertes.fr/hal-00924089

Publications of the year

Articles in International Peer-Reviewed Journals

• 11J. F. Bonnans, A. Festa.
  
  Error estimates for the Euler discretization of an optimal control problem with first-order state constraints, in: SIAM Journal on Numerical Analysis, December 2017, vol. 55, n^o 2, pp. 445–471.
  
  https://hal.inria.fr/hal-01093229
• 12M. D. Chekroun, A. Kröner, H. Liu.
  
  Galerkin approximations of nonlinear optimal control problems in Hilbert spaces , in: Electronic Journal of Differential Equations, 2017, vol. 2017, n^o 189, pp. 1-40.
  
  https://hal.archives-ouvertes.fr/hal-01501178
• 13J. Garcke, A. Kröner.
  
  Suboptimal feedback control of PDEs by solving HJB equations on adaptive sparse grids, in: Journal of Scientific Computing, January 2017, vol. 70, n^o 1, pp. 1-28.
  
  https://hal.archives-ouvertes.fr/hal-01185912
• 14B. Heymann, J. F. Bonnans, P. Martinon, F. Silva, F. Lanas, G. Jimenez.
  
  Continuous Optimal Control Approaches to Microgrid Energy Management, in: Energy Systems, 2017.
  
  https://hal.inria.fr/hal-01129393

International Conferences with Proceedings

• 15J. F. Bonnans, B. Gregorutti, P. Martinon, C. Rommel.
  
  Aircraft Dynamics Identification for Optimal Control, in: EUCASS 2017, Milan, Italy, R. Martinez-Val, C. Bonnal, D. Knight (editors), July 2017. [ DOI : 10.13009/EUCASS2017-179 ]
  
  https://hal.inria.fr/hal-01639731

Internal Reports

• 16M. D. Chekroun, A. Kröner, H. Liu.
  
  Galerkin approximations for the optimal control of nonlinear delay differential equations, Inria, 2017.
  
  https://hal.archives-ouvertes.fr/hal-01534673

Other Publications

• 17J. F. Bonnans, J. Gianatti, F. J. Silva.
  
  On the time discretization of stochastic optimal control problems: the dynamic programming approach, February 2017, working paper or preprint.
  
  https://hal.inria.fr/hal-01474285
• 18J. F. Bonnans, A. Kröner.
  
  Variational analysis for options with stochastic volatility and multiple factors, April 2017, working paper or preprint.
  
  https://hal.inria.fr/hal-01516011
• 19A. Kröner, A. Picarelli, H. Zidani.
  
  Infinite Horizon Stochastic Optimal Control Problems with Running Maximum Cost, October 2017, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01585766
• 20P. Martinon, P. Picard, A. Raj.
  
  On the Design of Optimal Health Insurance Contracts under Ex Post Moral Hazard, 2017, working paper or preprint.
  
  https://hal-polytechnique.archives-ouvertes.fr/hal-01348551

References in notes

• 21M. Bardi, I. Capuzzo-Dolcetta.
  
  Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations, Systems and Control: Foundations and Applications, Birkhäuser, Boston, 1997.
• 22G. Barles.
  
  Solutions de viscosité des équations de Hamilton-Jacobi, Mathématiques et Applications, Springer, Paris, 1994, vol. 17.
• 23T. Bayen, F. Mairet, P. Martinon, M. Sebbah.
  
  Analysis of a periodic optimal control problem connected to microalgae anaerobic digestion, in: Optimal Control Applications and Methods, 2014. [ DOI : 10.1002/oca.2127 ]
  
  https://hal.archives-ouvertes.fr/hal-00860570
• 24G. Bliss.
  
  Lectures on the Calculus of Variations, University of Chicago Press, Chicago, Illinois, 1946.
• 25J. F. Bonnans, J. Laurent-Varin.
  
  Computation of order conditions for symplectic partitioned Runge-Kutta schemes with application to optimal control, in: Numerische Mathematik, 2006, vol. 103, n^o 1, pp. 1–10.
• 26J. F. Bonnans, E. Ottenwaelter, H. Zidani.
  
  Numerical schemes for the two dimensional second-order HJB equation, in: ESAIM: M2AN, 2004, vol. 38, pp. 723-735.
• 27J. F. Bonnans, H. Zidani.
  
  Consistency of generalized finite difference schemes for the stochastic HJB equation, in: SIAM J. Numerical Analysis, 2003, vol. 41, pp. 1008-1021.
• 28A. E. Bryson, Y.-C. Ho.
  
  Applied optimal control, Hemisphere Publishing, New-York, 1975.
• 29M. Crandall, P. Lions.
  
  Viscosity solutions of Hamilton Jacobi equations, in: Bull. American Mathematical Society, 1983, vol. 277, pp. 1–42.
• 30W. Hager.
  
  Runge-Kutta methods in optimal control and the transformed adjoint system, in: Numerische Mathematik, 2000, vol. 87, n^o 2, pp. 247–282.
• 31A. Ioffe, V. Tihomirov.
  
  Theory of Extremal Problems, North-Holland Publishing Company, Amsterdam, 1979, Russian Edition: Nauka, Moscow, 1974.
• 32J.-L. Lagrange.
  
  Mécanique analytique, Paris, 1788, reprinted by J. Gabay, 1989.
• 33E. Lee, L. Markus.
  
  Foundations of optimal control theory, John Wiley, New York, 1967.
• 34G. Leitmann.
  
  An introduction to optimal control, Mc Graw Hill, New York, 1966.
• 35R. Muñoz-Tamayo, P. Martinon, G. Bougaran, F. Mairet, O. Bernard.
  
  Getting the most out of it: Optimal experiments for parameter estimation of microalgae growth models, in: Journal of Process Control, 2014, vol. 24, n^o 6, pp. 991 - 1001. [ DOI : 10.1016/j.jprocont.2014.04.021 ]
  
  http://www.sciencedirect.com/science/article/pii/S095915241400122X
• 36L. Pontryagin, V. Boltyanski, R. Gamkrelidze, E. Michtchenko.
  
  The Mathematical Theory of Optimal Processes, Wiley Interscience, New York, 1962.
• 37L. Young.
  
  Lectures on the calculus of variations and optimal control theory, W. B. Saunders Co., Philadelphia, 1969.