Variational Data Assimilation : from optimal control to large scale data assimilation

In this chapter, the optimal control of systems governed by an ODE is studied quite briefly.

We refer to [26] for a full course on the subject; the present chapter follows closely the presentation done in [26].

First we present basic examples, next we define the notion of controllability and present the Kalman's condition. The most simple but very important case is studied more in details: linear model - quadratic cost function (LQ case).

In particular a proof of existence and uniqueness of the solution is given; and its characterization using the Pontryagin's maximum principle and the Hamiltonian.