An Accelerated Proximal Gradient-based Model Predictive Control Algorithm

TL;DR

This paper introduces an accelerated proximal gradient-based algorithm for model predictive control that improves convergence rates and outperforms existing solvers on small MPC problems.

Contribution

It presents a novel accelerated quadratic programming algorithm with a higher convergence rate based on polynomially chosen iterative parameters.

Findings

Achieves convergence rate of O(1/p^α) with α > 2.

Outperforms MOSEK and ECOS on small MPC problems.

Demonstrates effectiveness through numerical experiments.

Abstract

In this letter, an accelerated quadratic programming (QP) algorithm is proposed based on the proximal gradient method. The algorithm can achieve convergence rate $O(1/p^{\alpha})$, where $p$ is the iteration number and $\alpha$ is the given positive integer. The proposed algorithm improves the convergence rate of existing algorithms that achieve $O(1/p^{2})$. The key idea is that iterative parameters are selected from a group of specific high order polynomial equations. The performance of the proposed algorithm is assessed on the randomly generated model predictive control (MPC) optimization problems. The experimental results show that our algorithm can outperform the state-of-the-art optimization software MOSEK and ECOS for the small size MPC problems.