Automatic differentiation of Sylvester, Lyapunov, and algebraic Riccati equations
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Publication:6354344
arXiv2011.11430MaRDI QIDQ6354344
Author name not available (Why is that?)
Publication date: 23 November 2020
Abstract: Sylvester, Lyapunov, and algebraic Riccati equations are the bread and butter of control theorists. They are used to compute infinite-horizon Gramians, solve optimal control problems in continuous or discrete time, and design observers. While popular numerical computing frameworks (e.g., scipy) provide efficient solvers for these equations, these solvers are still largely missing from most automatic differentiation libraries. Here, we derive the forward and reverse-mode derivatives of the solutions to all three types of equations, and showcase their application on an inverse control problem.
Has companion code repository: https://github.com/tachukao/autodiff-inverse-lqr
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