Olivier Bokanowski
Associate Professor at University Paris Cité (Ex. Paris-Diderot / Paris 7)

 Laboratoire Jacques Louis Lions (UMR 7598)

 LJLL at UPC :
 Bureau 5024, UFR de Mathématiques
Bâtiment Sophie Germain, 8 place Aurélie Nemours 75205 Paris CEDEX 13

 LJLL at Sorbonne université (Ex.Univ. Pierre et Marie Curie / Paris 6)
(3rd floor) - 15-25 - 4, place Jussieu, Paris 5ème

Tel: (33) 1 57 27 91 19 ;  Sec:  (33) 1 57 27 xx xx  (92 95: secrétariat /  93 16: N. Bergame / 55 55: secrétariat)
 Email:   olivier.bokanowski at u-paris.fr

     

Current research interests
  • Hamilton-Jacobi-Bellman (HJB) equations for deterministic and stochastic optimal control, state constraints, reachability
  • Anti-diffusive schemes, discontinuous galerkin schemes, sparse and sparsegrids approaches for HJB equations, Neural networks
  • Industrial applications (space launchers, collision avoidance, trajectory planification)
 Simulations:

front propagation on Cat-k domains




Code (PDE Solver):  Parallel d-dimensional c++ solver for Reachability and Optimal Control using Hamilton-Jacobi equations Related groups:
  • Sensitivity Analysis for Deterministic Controller Design - SADCO
  • HJnet
  • COSS
    • Photo

    Research papers :
    • O. Bokanowski, X. Warin,  Neural networks for differential games, arXiv
    • O. Bokanowski, A. Prost, X. Warin,  Neural networks for first order HJB equations and application to front propagation with obstacle terms, arXiv Partial Differential Equations and Applications, 2023, vol. 4, issue 5, 1-36 link
    • O. Bokanowski, A. Désilles, H. Zidani, Relationship between maximum principle and dynamic programming in presence of intermediate and final state constraint, Esaim:COCV, vol 27 (2021) HAL
    • O. Bokanowski, N. Gammoudi, H. Zidani, Optimistic Planning Algorithms for State-Constrainted optimal control problems, Computers & Mathematics with Applications, 109(1):158-179, (2022) PDF  HAL
    • O. Bokanowski, A. Picarelli, C. Reisinger, Stability and convergence of second order backward differentiation schemes for parabolic Hamilton-Jacobi-Bellman equations  Numerische Mathematik (2021)  HAL
    • O. Bokanowski, K. Debrabant, BDF finite difference schemes for diffusion equations with an obstacle term. IMA J. of Numerical Analysis,  41(2):900–934 (2021), link  HAL
    • R. Baier, O. Bokanowski, M. Gerdts, I. Xausa, Computation of avoidance regions for driver assistance systems by using a Hamilton-Jacobi approach. Optim Control Appl Meth (OCAM) 41(2): 668-689 (2020) HAL link
    • O. Bokanowski, E. Bourgeois, A. Désilles, H. Zidani, New improvements in the optimization of the launcher ascent trajectory through the HJB approach. Proceedings EUCASS 2017
    • O. Bokanowski, A. Picarelli, C. Reisinger, High-order filtered schemes for time-dependent second order HJB equations. ESAIM:M2AN 52(1):69-97 (2018)  link  HAL
    • M. Assellaou, O. Bokanowski, A. Désilles, H. Zidani, Value function and optimal trajectories for a maximum running cost control problem with state constraints. Application to an abort landing problem. ESAIM: M2AN 52(1):305-335 (2018) link
    • O. Bokanowski, E. Bourgeois, A. Désilles, H. Zidani, Payload optimization for multi-stage launchers using HJB approach and application to a SSO mission. Proceedings, 20th IFAC, 2017 pdf
    • M. Assellaou, O. Bokanowski, A. Désilles, H. Zidani, A Hamilton-Jacobi-Bellman approach for the optimal control of an abort landing problem. Proceedings of Decision and Control (CDC), 2016 IEEE 55th. pdf
    • O. Bokanowski, E. Bourgeois, A. Désilles, H. Zidani, Global optimization approach for the climbing problem of multi-stage launchers. Proc. 7th Int. Conf. on High Performance Scientific Computing (2018) hal
    • O. Bokanowski, E. Bourgeois, A. Désilles, H. Zidani, Optimization of the launcher ascent trajectory leading to the global optimum without any initialization: the breakthrough of the HJB approach. Proceeding EUCASS 2015  6th European Conference for Aeronautics and Space Sciences.
    • O. Bokanowski, A. Picarelli, H. Zidani, State-constrained stochastic optimal control problems via reachability approach. SICON, Vol. 54(5), pp. 2568-2593 (2016)  pdf
    • O. Bokanowski, M. Falcone, S. Sahu,  An efficient filtered scheme for some first order Hamilton-Jacobi-Bellman equations. SIAM J. Sci. Comput., 38(1), A171-A195, 2016. pdf
    • O. Bokanowski, G. Simarmata, Semi-Lagrangian discontinuous galerkin schemes for some first and second order PDEs. ESAIM: M2AN,  Vol. 50, pp. 1699-1730, 2016.  doi: 10.1051/m2an/2016004 pdf
    • O. Bokanowski, Y. Cheng, C.-W. Shu,  Convergence of discontinuous Galerkin schemes for front propagation with obstacles. Math. Comp. 2016, link pdf
    • O. Bokanowski, A. Picarelli, H. Zidani, Dynamic programming and error estimates for stochastic control problems with maximum cost. Applied Math. Optim., Feb 2015, Vol 71 (1), pp 125-163. pdf
    • O. Bokanowski, M. Falcone, R. Ferretti, L. Grüne, D. Kalise, H. Zidani, Value iteration convergence of epsilon-monotone schemes for stationnary HJ equations. DCDS-A Vol 35 (9), pp 4041-4070 (2015). pdf
    • M. Assellaou, O. Bokanowski and  H. Zidani, Error estimates for second order HJB equations. Approximation of probabilistic reachable sets. DCDS-A Vol 35 (9), pp 3933--3964 (2015). pdf
    • O. Bokanowski, Y. Cheng, C.-W. Shu,  A discontinuous Galerkin scheme for front propagation with obstacles,  Numerische Math., 126(1), pp. 1-31 (2014)  pdf
    • A. Altarovici, O. Bokanowski, H. Zidani,  A general HJ framework  for state-constrained control problems,  COCV, Vol. 19 (2), pp. 337-357 (2013) pdf
    • O. Bokanowski, J. Garcke, M. Griebel, I. Klompmaker, An adaptive sparsegrid semi-Lagrangian scheme for front propagation. J. Scient. Comput. 55 (3), pp.575–605 (2013) pdf
    • Y. Achdou, O. Bokanowski, T. Lelievre, Partial Differential  Equations in finance. The Encyclopedia of Financial Models, John Wiley & Sons, F. Fabozzi Ed., 2012 pdf
    • O. Bokanowski, E. Cristiani, J. Laurent-Varin, H. Zidani.   HJB approach for the climbing problem for heavy launchers. Proceedings of the MTNS conference, 2012. pdf  (full version)
    • O. Bokanowski, N. Forcadel, H. Zidani,  Deterministic state constrained optimal control problems without controllability assumptions. COCV,  Vol. 17, 995-1015. (2011) pdf
    • O. Bokanowski, Y. Cheng, C.-W. Shu,  A discontinuous galerkin solver for front propagation, SIAM J. Scient. Comput. 33 (2), 923-938 (2011)  pdf
    • O. Bokanowski, H. Zidani, Minimal time problems with moving targets and obstacles, 18th IFAC Proceedings, pp.  2590-2593 (2011) pdf
    • O. Bokanowski, A. Désilles, H. Zidani, HJB approach for motion planning and reachability analysis, VALUETOOLS '11: Proceedings. pdf
    • O. Bokanowski, E. Cristiani and H. Zidani,  An efficient data structure and accurate scheme to solve front propagation problems J. Sci. Computing, Vol. 42, No. 10, pp. 251-273 (2010) pdf.
    • O. Bokanowski, N. Megdich, H. Zidani, Convergence of a non-monotone scheme for HJB equations with discontinous initial data, Numerische Math., Vol 115, No. 1, pp. 1-44 (2010)  pdf.
    • O. Bokanowski, N. Forcadel, H. Zidani,   L¹-error estimate for numerical approximations of Hamilton-Jacobi-Bellman equations in dimension 1. Math. Comp. 79, 1395-1426 (2010) pdf. 
    • O. Bokanowski, N. Forcadel, H. Zidani,  Reachability and minimal times for state constrained nonlinear problems without any controllability assumption. SIAM J. Control Optim. 48(7), 4292-4316 (2010) pdf.
    • O. Bokanowski, B. Bruder, S. Maroso, H. Zidani,  Numerical approximation for a superreplication problem under gamma constraints.  SIAM J. Numer. Anal. Vol. 47 (3), pp. 2289-2320 (2009) pdf. 
    • O. Bokanowski, S. Maroso, H. Zidani, Some convergence results for Howard's algorithm.    SIAM J. Numer. Anal. Volume 47, Issue 4, pp. 3001-3026 (2009)
    • R. Pino, O. Bokanowski, E. V. Ludena, R. Lopez-Boada.  Analysis of the Stability of Finite Subspaces in Density Functional Theory.  Theor. Chem. Accounts 123 pp. 189--196  (2009) pdf.
    • O. Bokanowski, E. Cristiani, J. Laurent-Varin, H. Zidani.   Trajectory optimization of launcher with HJB approach. Proceeding Eucass.
    • O. Bokanowski, A. Briani, H. Zidani,  Minimum time control problems for non autonomous differential equations.  Systems & Control Letters, Volume 58, Issues 10-11, pp. 742-746.  (2009) pdf.
    • O. Bokanowski, H. Zidani, Anti-dissipative schemes for advection and application to HJB equations J. Scient. Computing, Vol. 30, No. 1, pp. 1-33 (2007) pdf.
    • R. Pino, O. Bokanowski, E. V. Ludena, R. Lopez-Boada, A re-statement of the Hohenberg-Kohn theorem and its extension to finite subspaces,   Theo. Chem. Accounts, Vol 118 (3), pp. 557-561 (2007)
    • O. Bokanowski, S. Martin, R. Munos, H. Zidani,   An anti-diffusive scheme for viability problems,   Applied Numerical Mathematics, Volume 56, Issue 9, pp. 1147-1162 (2006)  pdf
    • O. Bokanowski, N. Megdich & H. Zidani,   An adaptative antidissipative method for optimal control problems, Revue ARIMA, Vol 5, 256-271 (2006) pdf
    • O. Bokanowski, J-L. Lopez, O. Sanchez & J. Soler,   Long time behaviour to the Schrödinger--Poisson--X-alpha systems,   Lecture Note in Physics,  pp. 217-232, Vol 690 (2006) pdf
    • ... etc.

    Contracts, applied collaborations

    - 2021-2024: PGMO "Neural networks and decomposition strategies for Bellman equations"

    - 2017-2019: CNES/ENSTA

    - 2015-2017: DGA/ENSTA

    - 2012-2015: DGA/ENSTA, Planification de trajectoire par approche HJB : atteignabilité et évitement d'obstacle", with H. Zidani & A. Desilles

    - 2009-2011:  HPC Project / INRIA "BiNoPe-HJ:  original numerical libraries for HJ equations", with H. Zidani & N. Forcadel

    - 2006-2010: CNES/INRIA, "HJB approach for trajectory optimisation for space launchers" with H. Zidani & P. Martinon




    Teaching ==> ooo <==

    All truth passes through three stages :
    First, it is ridiculed
    Second, it is violently opposed
    Third, it is accepted as being self-evident
    (Schopenhauer 1788-1860)



    Example of target problems (animations)

    Car target problem with obstacles
    With drift
     More obstacles, and drift

    Moving target and obstacle

    Reachable set with obstacle