Model predictive control in combination with discrete time non-linear observer theory is studied in this paper. Model predictive control, generally based on state space models, needs the complete state for feedback. In this paper the complete state is assumed not to be known and only outputs and inputs of the system are measured. To obtain knowledge of the full state an observer is used to obtain an estimate of the state. An extended non-linear observer is used for thispurpose and potentially allows for successfuloutput-based model predictive controllers.