# Preconditioned warm-started Newton-Krylov methods for MPC with discontinuous control

## TL;DR

This paper introduces preconditioned Newton-Krylov methods tailored for solving optimal control problems with discontinuous controls in model predictive control, demonstrating efficient computation and the benefits of warm-start strategies.

## Contribution

The work develops and tests Newton-Krylov methods with preconditioning and warm-start techniques for discontinuous control problems in MPC, achieving near-optimal computational complexity.

## Key findings

- GMRES with preconditioning achieves O(N) complexity.
- Warm-starting along the horizon improves convergence.
- Method successfully applied to a double integrator minimum-time problem.

## Abstract

We present Newton-Krylov methods for efficient numerical solution of optimal control problems arising in model predictive control, where the optimal control is discontinuous. As in our earlier work, preconditioned GMRES practically results in an optimal $O(N)$ complexity, where $N$ is a discrete horizon length. Effects of a warm-start, shifting along the predictive horizon, are numerically investigated. The~method is tested on a classical double integrator example of a minimum-time problem with a known bang-bang optimal control.