An Iterative Horizon-Splitting Method for Model Predictive Control

This paper presents a simple iterative method for linear model predictive control (MPC). Approximate value functions requiring only first-order derivatives and incorporating fixed second-order information are used, which leads to a method that splits the MPC problem into subproblems along the prediction horizon, and only the states and costates (Lagrange multipliers corresponding to the state equations) are exchanged between consecutive subproblems during iteration. The convergence is guaranteed under the framework of the majorization-minimization principle. The performance of the proposed method was assessed against both first- and second-order methods with two numerical experiments. The results indicate that the proposed method can obtain a moderately accurate solution with a small number of inexpensive iterations.