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 employs 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. 1. INTRODUCTION In this paper we analyze the parallel solution of the linear-quadratic (LQ) optimal control problem for periodic control systems on parallel computers with distributed memory. Specifically, we consider the discrete-time linear control system