Appendix
Optimal control : a new approach to improve image quality in MRI

• Towards a Hamiltonian formulation of OCT: Pontryagin's maximum principle

In this supplement, we show the origin of the Hamiltonian formulation of Pontryagin's maximum principle in a simple case where there are no constraints on the control field and the final time is fixed. To simplify calculations, we will only consider first-order variations. For the general case, the reference is a very good introduction for an engineering audience.

Consider the dynamic system described by the following nonlinear differential...