Decoupling Optimal Control Problems via Simultaneous Block Diagonalization of Matrices

In this paper, we consider optimal control problems (OCPs) applied to large-scale linear dynamical systems with many states and many inputs and a quadratic objective function. We implement the method of simultaneous block diagonalization of matrices (SBD) to decouple these problems into subproblems of lower dimensions with no loss of information. We provide an example for which we break a large OCP involving 141 coupled second-order systems into 114 independent OCPs, each described by a lower-dimensional system and an associated cost function.