Solving Large-Scale Control Problems

Sparsity and parallel algorithms: two approaches to beat the curse of dimensionality. By Peter Benner I n 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 trunca-tion model reduction using either parallel computing or sparse matrix algo-rithms. 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 engi-neers can employ complex models and use computational tools to analyze and design feedback control laws. Backgroun