A Numerical Comparison of Different Solvers for Large-Scale, Continuous-Time Algebraic Riccati Equations and LQR Problems
Peter Benner, Zvonimir Bujanović, Patrick Kürschner, Jens Saak
Abstract
In this paper, we discuss numerical methods for solving large-scale<br>continuous-time algebraic Riccati equations. These methods have been the focus<br>of intensive research in recent years, and significant progress has been made<br>in both the theoretical understanding and efficient implementation of various<br>competing algorithms. There are several goals of this manuscript: first, to<br>gather in one place an overview of different approaches for solving large-scale<br>Riccati equations, and to point to the recent advances in each of them. Second,<br>to analyze and compare the main computational ingredients of these algorithms,<br>to detect their strong points and their potential bottlenecks. And finally, to<br>compare the effective implementations of all methods on a set of relevant<br>benchmark examples, giving an indication of their relative performance.<br>