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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

2020MPG.PuRe (Max Planck Society)36 citationsOpen Access PDF

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>

Topics & Concepts

MathematicsAlgebraic Riccati equationApplied mathematicsRiccati equationLinear-quadratic regulatorScale (ratio)Algebraic numberNumerical analysisAlgebraic equationOptimal controlMathematical optimizationMathematical analysisPartial differential equationNonlinear systemQuantum mechanicsPhysicsModel Reduction and Neural NetworksNumerical methods for differential equationsMatrix Theory and Algorithms
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