# Least squares dynamics in Newton-Krylov Model Predictive Control

## TL;DR

This paper introduces a least squares approach within Newton-Krylov methods for nonlinear Model Predictive Control, offering an alternative to Ohtsuka's C/GMRES that handles inconsistent constraints effectively.

## Contribution

It proposes a novel least squares formulation for Newton-Krylov methods in MPC, improving robustness when constraints are inconsistent.

## Key findings

- Numerical tests confirm the effectiveness of the proposed method.
- The approach handles constraint inconsistencies better than existing methods.
- Modified Newton-Krylov methods show promising results in simulations.

## Abstract

Newton-Krylov methods for nonlinear Model Predictive Control are pioneered by T. Ohtsuka under the name "C/GMRES". Ohtsuka eliminates a system state over the horizon from Karush-Kuhn-Tucker stationarity conditions of a Lagrangian using equations of system dynamics. We propose instead using least squares to fit the state to the dynamics and some constraints on the state, if they are inconsistent. Correspondingly modified Newton-Krylov methods are described. Numerical tests demonstrate workability of our modification.