Abstract: For the exo-atmospheric interception,the model predictive control(MPC) of nonlinear systems with uncertainty and on-off inputs is studied.The Fliess functional expansion is used to describe the relationship between the outputs and both control inputs and uncertainty.Using the quadratic criterion,the optimal control problem of MPC is obtained.In order to deal with the uncertainty in criteria,a solving method of optimization,which uses nonlinear programming and combines the characteristic of on-off inputs,is proposed.Finally,the method is applied to exo-atmospheric interception.In the case of an uncertain relative distance and the rate of line-of-sight,the on-off guidance law is designed.The simulation results show that the proposed method guarantees high interception accuracy and reduces the on-off times of the thruster.