On considere plusieurs problemes de controle optimal gouvernes par des equations elliptiques d'ordre 2 (dont certaines a coefficients rapidement oscillants). Dans la fonction cout, le coefficient de la norme du controle tend vers 0, d'ou la terminologie ''controle bon marche''. On etudie le comportement asymptotique quand ->0.
We consider several optimal control problems governed by second order elliptic equations, some of which have rapidly oscillating coefficients. In the cost functional, the coefficient of the norm of the control tends to 0, hence the terminology ''low cost control''. The asymptotic behaviour as ->0 is studied.