Research interests
-
Hamilton-Jacobi-Bellman
(HJB) equations for deterministic and
stochastic optimal control, state
constraints, reachability, games
- 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-kappa and
non-Cat-kappa domains
Photo
Research papers :
- O. Bokanowski, X. Warin, Representation
results and error estimates for
differential games with
applications using neural
networks,Dynamic
Games and Applications 2024.(arXiv) Link
- O. Bokanowski, A. Prost, X.
Warin, Neural networks
for first order HJB equations
and application to front
propagation with obstacle terms, Partial
Differential Equations and
Applications, 2023, vol. 4,
issue 5, 1-36 link
(arXiv)
- 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
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)