Solving large-scale control problems

In this article we discuss sparse matrix algorithms and parallel algorithms, as well as their application to large-scale systems. For illustration, we solve the linear-quadratic regulator (LQR) problem and apply balanced truncation model reduction using either parallel computing or sparse matrix algorithms. We conclude that modern tools from numerical linear algebra, along with careful investigation and exploitation of the problem structure, can be used to derive algorithms capable of solving large control problems. Since these approaches are implemented in production-quality software, control engineers can employ complex models and use computational tools to analyse and design feedback control laws.