Sparse preconditioning for model predictive control

TL;DR

This paper introduces an efficient O(N) preconditioning technique to accelerate the iterative solution of nonlinear systems in model predictive control, enhancing the Continuation/GMRES method's performance.

Contribution

It presents a novel preconditioning approach that significantly reduces computational complexity for solving MPC-related systems, improving existing Newton-Krylov methods.

Findings

Achieves linear O(N) complexity in preconditioning

Speeds up convergence of Newton-Krylov methods

Applicable to nonlinear and linear systems in MPC

Abstract

We propose fast O(N) preconditioning, where N is the number of gridpoints on the prediction horizon, for iterative solution of (non)-linear systems appearing in model predictive control methods such as forward-difference Newton-Krylov methods. The Continuation/GMRES method for nonlinear model predictive control, suggested by T. Ohtsuka in 2004, is a specific application of the Newton-Krylov method, which uses the GMRES iterative algorithm to solve a forward difference approximation of the optimality equations on every time step.