  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.
