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A Numerical Comparison of Different Solvers for Large-Scale, Continuous-Time Algebraic Riccati Equations and LQR Problems

In this paper, we discuss numerical methods for solving large-scale continuous-time algebraic Riccati equations. These methods have been the focus of intensive research in recent years, and significant progress has been made in both the theoretical understanding and efficient implementation of various competing algorithms. There are several goals of this manuscript. The first is to gather in one place an overview of different approaches for solving large-scale Riccati equations, and to point to the recent advances in each of them. The second goal is to analyze and compare the main computational ingredients of these algorithms and to detect their strong points and their potential bottlenecks. Finally, we want to compare the effective implementations of all methods on a set of relevant benchmark examples, giving an indication of their relative performance.

algebraic Riccati equation ; Lyapunov equation ; alternating direction implicit ; rational Krylov subspaces ; Newton’s method

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