Master Course on Optimal Control of
Partial Differential Equations by
Frédéric Bonnans
Specialized course of the
Optimization master , Inst. Pol. Paris and U. ParisSaclay;
AMS master, U. ParisSaclay;
Mathematics of modelization, Sorbonne Université,
majeure COCV.
Course codes: EN4726 (Optim.), EN5340 (AMS).
Location: LMO (Lab. Math. Orsay),
Orsay Campus, building 307, room 1B14.
Schedule for 2023: February 14, 21, 28;
March 07, 14, 21, from 2 to 5 pm.
Exam on March 28,
25pm
(details given later).
As a motivation for the optimal control of PDEs,
we will present the
optimization problem of protein production based on gene expression
thanks to the messenger RNA (mRNA). There is currently an increased
interest for this type of technique, which however raises serious
difficulties for the mathematical / numerical analysis.
We will show how to express the original problem
as an optimal control problem for the FokkerPlanck
equation. The latter is a conservative, anisotropic parabolic PDE, with
degeneracies at the boundary and control through the
coefficients. We will discuss the wellposedness of this PDE
(in appropriate weighted spaces) and the approximation of
related optimal control problems by finite difference methods.
USEFUL REFERENCES

J.L. Lions:
Optimal Control of Systems Governed by Partial
Differential Equations.
Springer, 1971.