ADMM for Block Circulant Model Predictive Control
This work addresses computational efficiency in model predictive control for large-scale systems with cyclic symmetry, which is a specific domain problem.
The paper introduces a complex-valued coordinate transformation for block circulant systems that block diagonalizes and truncates the finite-horizon optimal control problem, and develops a modified ADMM algorithm that significantly increases computation speed in simulated examples.
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.