The shooting approach to optimal control problems.

Summary We give an overview of the shooting technique for solving deterministic optimal control problems. This approach allows to reduce locally these problems to a finite dimensional equation. We first recall the basic idea, in the case of unconstrained or control constrained problems, and show the link with second-order optimality conditions and the analysis or discretization errors. Then we focus on two cases that are now better undestood: state constrained problems, and affine control systems. We end by discussing extensions to the optimal control of a parabolic equation.