A parallel Newton-type method for nonlinear model predictive control

Abstract

A parallel Newton-type method for nonlinear model predictive control is presented that exploits the particular structure of the associated discrete-time Euler–Lagrange equations obtained by utilizing an explicit discretization method in the reverse-time direction. These equations are approximately decoupled into single-step subproblems along the prediction horizon for parallelization. The coupling variable of each subproblem is approximated to its optimal value using a simple, efficient, and effective method at each iteration. The rate of convergence of the proposed method is proved to be superlinear under mild conditions. Numerical simulation of using the proposed method to control a quadrotor showed that the proposed method is highly parallelizable and converges in only a few iterations, even to a high accuracy. Comparison of the proposed method’s performance with that of several state-of-the-art methods showed that it is faster.