A Warm-Start Strategy in Interior Point Methods for Shrinking Horizon Model Predictive Control With Variable Discretization Step

In this article, we present a warm-start point algorithm in interior point methods for shrinking horizon model predictive control with a variable discretization step. In the algorithm, a convex combination of components of the earlier optimal solution is used to construct an interpolation point, and we use the convex combination of the modified interpolation point and the cold-start point to obtain a warm-start point. We prove that the worst-case iteration complexity of our strategy is better than that of the cold-start. In the numerical experiment of fuel-optimal planetary powered-descent guidance problems, our strategy reduces the number of iterations of second-order cone programming by about 80% with the number of samples available in practical applications.