Algebraic Decomposition of Model Predictive Control Problems

This paper is concerned with the application of model predictive control (MPC) to large-scale linear dynamical systems with linear inequality constraints. A decomposition is proposed of such problems into sets of independent MPCs of lower dimensions that preserves all information about the system, cost function, and constraints. Different from previous work, the constraints are incorporated in the decomposition procedure, which is attained by generalizing a previously developed technique to simultaneously block diagonalize a set of matrices. This approach is applied to practical examples involving large-scale systems with inequality constraints. It is shown that the computational complexity and the CPU time required to solve the transformed MPC problems are lower than those required by the solution of the original MPC problem.