ADMM for Block Circulant Model Predictive Control

TL;DR

This paper introduces a novel coordinate transformation and an adapted ADMM algorithm to efficiently solve large-scale, cyclically symmetric model predictive control problems, significantly improving computation speed.

Contribution

It presents a new complex-valued coordinate transformation that block diagonalizes the problem, enabling faster ADMM-based solutions for block circulant MPC problems.

Findings

Coordinate transformation significantly speeds up computation

Modified ADMM effectively handles constrained quadratic programs

Demonstrated efficiency gains in simulated examples

Abstract

This paper deals with model predictive control problems for large scale dynamical systems with cyclic symmetry. Based on the properties of block circulant matrices, we introduce a complex-valued coordinate transformation that block diagonalizes and truncates the original finite-horizon optimal control problem. Using this coordinate transformation, we develop a modified alternating direction method of multipliers (ADMM) algorithm for general constrained quadratic programs with block circulant blocks. We test our modified algorithm in two different simulated examples and show that our coordinate transformation significantly increases the computation speed.