# Towards parallelizable sampling-based Nonlinear Model Predictive Control

## TL;DR

This paper introduces a parallelizable sampling-based nonlinear MPC algorithm that guarantees stability and feasibility, with complexity quadratic in the horizon and linear in samples, suitable for real-time control.

## Contribution

The paper presents a novel sampling-based nonlinear MPC method that enables parallel computation and guarantees recursive feasibility and stability.

## Key findings

- Algorithm converges rapidly to near-optimal solutions.
- Complexity depends only on horizon, samples, and threads.
- Performs well compared to traditional nonlinear solvers.

## Abstract

This paper proposes a new sampling-based nonlinear model predictive control (MPC) algorithm, with a bound on complexity quadratic in the prediction horizon N and linear in the number of samples. The idea of the proposed algorithm is to use the sequence of predicted inputs from the previous time step as a warm start, and to iteratively update this sequence by changing its elements one by one, starting from the last predicted input and ending with the first predicted input. This strategy, which resembles the dynamic programming principle, allows for parallelization up to a certain level and yields a suboptimal nonlinear MPC algorithm with guaranteed recursive feasibility, stability and improved cost function at every iteration, which is suitable for real-time implementation. The complexity of the algorithm per each time step in the prediction horizon depends only on the horizon, the number of samples and parallel threads, and it is independent of the measured system state. Comparisons with the fmincon nonlinear optimization solver on benchmark examples indicate that as the simulation time progresses, the proposed algorithm converges rapidly to the "optimal" solution, even when using a small number of samples.