A Parallel Riccati Factorization Algorithm with Applications to Model Predictive Control

TL;DR

This paper introduces a non-iterative parallel Riccati factorization algorithm tailored for Model Predictive Control, significantly reducing computation time by exploiting problem structure and enabling efficient parallel processing.

Contribution

A novel parallel Riccati factorization algorithm that scales logarithmically with prediction horizon, improving computational efficiency in MPC applications.

Findings

Algorithm exploits MPC problem structure.

Complexity scales logarithmically with horizon.

Reduces computation cost in MPC algorithms.

Abstract

Model Predictive Control (MPC) is increasing in popularity in industry as more efficient algorithms for solving the related optimization problem are developed. The main computational bottle-neck in on-line MPC is often the computation of the search step direction, i.e. the Newton step, which is often done using generic sparsity exploiting algorithms or Riccati recursions. However, as parallel hardware is becoming increasingly popular the demand for efficient parallel algorithms for solving the Newton step is increasing. In this paper a tailored, non-iterative parallel algorithm for computing the Riccati factorization is presented. The algorithm exploits the special structure in the MPC problem, and when sufficiently many processing units are available, the complexity of the algorithm scales logarithmically in the prediction horizon. Computing the Newton step is the main computational bottle-neck in many MPC algorithms and the algorithm can significantly reduce the computation cost for popular state-of-the-art MPC algorithms.