A nonlinear model predictive control using a continuation method and a step input constraint

The nonlinear model predictive control (MPC) needs to solve a two-point boundary-value problem (TP-BVP) at every sample time based on the receding horizon control strategy. However, solving a nonlinear algebraic equation for the TP-BVP requires high computational load, so developing an efficient computation method of the control law in real-time is a significant issue on the research of the nonlinear model predictive control. This paper proposes an efficient calculation method of the control law for nonlinear MPC. The proposed approach searches an optimal step-type input signal for a given performance index beforehand, then the input signal is successively updated using a continuation method. Hence, it can reduce the computation load because the number of the parameter to be optimized becomes one in the SISO case or the number of the inputs in the MIMO case, and solving TP-BVP can be avoided by a continuation method. In addition, the accuracy of the nonlinear algebraic equation, which gives the optimal condition, keeps well by analytically deriving the updating law of the MPC control law. A numerical example shows that the proposed method can reduce the computation load of the nonlinear MPC, while the accuracy of the optimal conditions given by the nonlinear algebraic equations keeps a tolerance level.