Abstract : This series of notes have their origin into accelerated course in optimal control given
to multidisciplinary Phd students in Mathematics, Physics or Control Engineering
and the purpose is to present the seminal results of this theory in view of applications
to concrete problems. For that we choose to make the presentation using two real
life applications which are the core of current research projects on the academic side
and motivated by industrial applications. The two applications concern the swimming at
low Reynolds number and the contrast problem in Magnetic Resonance Imaging.