Parallel Algorithms for LQ Optimal Control of Discrete-Time Periodic Linear Systems

This paper analyzes the performance of two parallel algorithms for solving the linear-quadratic optimal control problem arising in discrete-time periodic linear systems. The algorithms perform a sequence of orthogonal reordering transformations on formal matrix products associated with the periodic linear system and then employ the so-called matrix disk function to solve the resulting discrete-time periodic algebraic Riccati equations needed to determine the optimal periodic feedback. We parallelize these solvers using two different approaches, based on a coarse-grain and a medium-grain distribution of the computational load. The experimental results report the high performance and scalability of the parallel algorithms on a Beowulf cluster.