Inexact Newton–Kantorovich Methods for Constrained Nonlinear Model Predictive Control

In this paper, we consider Newton–Kantorovich type methods for solving control-constrained optimal control problems that appear in model predictive control. Conditions for convergence are established for an inexact version of the Newton–Kantorovich method applied to variational inequalities. Based on these results, two groups of algorithms are proposed to solve the optimality system. The first group includes exact and inexact Newton and Newton–Kantorovich implementations of the sequential quadratic programming. In the second group, exact and inexact Newton and Newton–Kantorovich methods are developed for solving a nonsmooth normal map equation equivalent to the optimality system. Numerical simulations featuring examples from the aerospace and automotive domain are presented, which show that inexact Newton–Kantorovich type methods can achieve significant reduction of the computational time.