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The research I intend to follow is concerned
with optimal control
theory and shape optimization. One main issue in optimal
control theory is to find properties of optimal trajectories for
differential controlled systems (in terms of optimal feedback control
laws) via Pontryagin maximum principle and Hamilton-Jacobi equation.
Several differential systems (in connection with bioprocesses) for
which singular strategies can be defined lead to interesting studies.
The second aspect I intend to develop deals with non standard shape optimization problems
(for instance involving convex constraints) for which standard methods
(such as Euler-Lagrange equation in calculus of variation) cannot be
applied. One interesting issue is to find adequate way to formulate convexity constraints within an optimization problem.