Model Predictive Control with Cross-Product Term between State and Input

Model Predictive Control (MPC) is one of control methods for the discrete time system. The optimum input is calculated by using Linear Quadratic Regulator (LQR). In MPC, the cross-product term is generally omitted in the evaluation function for LQR. However, the effectiveness of the cross-product term for LQR is confirmed by various researches. Therefore, this paper addresses the expanded form of cross-product term applied to MPC. Simulation of zero momentum spacecraft shows that the cross-product term is effective for consideration of performance to MPC.