Nonlinear MPC with time-varying terminal cost for tracking unreachable periodic references

In this paper, nonlinear model predictive control is investigated for a nonlinear system using a time-varying terminal cost function. An artificial reference and a control input are added as decision variables for tracking an unreachable periodic reference. Some constraints are given in an optimization problem to guarantee feasibility if the periodic references change suddenly for the reason of that the constraints are independent on the periodic references. A time-varying periodic polytopic linear difference inclusion is proposed to guarantee behavior locally around the artificial reference of the nonlinear system. A time-varying weight matrix is designed for the time-varying terminal cost function to ensure stability of the nonlinear system. Effectiveness of the developed tracking control scheme is shown by a simulation example on a mobile robot system.