This paper deals with the moving horizon estimation and predictive control synthesis of a Pantograph-Catenary (PAC) system. The pantograph is the element of the train that collects electric current from the overhead line, the catenary. At high speeds, the contact between the pantograph and the catenary becomes less and less consistent resulting in poor current collection performance. This variation produces coupling and uncoupling from the electrical network, which may further cause power losses, electric arc formations and important perturbations in the entire electrical network. Most nowadays train systems use passive elements to limit the variations of the contact. This paper proposes a closed loop control of contact force using a Model Predictive Control (MPC) strategy for the control and a Moving Horizon Estimation (MHE) for the observer.