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A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces
ArticleAbstract: We present an approximation framework for computing the solution of the stochastic linear quadraticPalabras claves:Approximation schemes, feedback control, Riccati equations, Stochastic linear quadratic regulator problemsAutores:Hermann Mena, Levajkovic T., Tuffaha A.Fuentes:scopusA splitting/polynomial chaos expansion approach for stochastic evolution equations
ArticleAbstract: In this paper, we combine deterministic splitting methods with a polynomial chaos expansion method fPalabras claves:Analytic semigroups, Fourier–Legendre polynomials, Polynomial chaos expansion, Resolvent splitting, splitting methods, Wiener–Legendre expansionAutores:Hermann Mena, Kofler A., Levajkovic T., Ostermann A.Fuentes:scopusApplications and Numerical Approximation
Book PartAbstract: In this chapter we present applications of the chaos expansion method in optimal control and stochasPalabras claves:Autores:Hermann Mena, Levajkovic T.Fuentes:scopusNumerical low-rank approximation of matrix differential equations
ArticleAbstract: The efficient numerical integration of large-scale matrix differential equations is a topical problePalabras claves:Differential Lyapunov equations, Differential Riccati equations, Dynamical low-rank approximation, El Niño simulation, Linear quadratic regulator problem, Splitting integratorsAutores:Hermann Mena, Lena Maria Pfurtscheller, Ostermann A., Piazzola C.Fuentes:scopusRosenbrock methods for solving riccati differential equations
ArticleAbstract: The Riccati differential equation (RDE) arises in several fields like optimal control, optimal filtePalabras claves:Linear-implicit Runge-Kutta, Riccati differential equation, Rosenbrock methods, Sylvester equationAutores:Benner P., Hermann MenaFuentes:scopusThe stochastic linear quadratic optimal control problem in hilbert spaces: A polynomial chaos approach
ArticleAbstract: We consider the stochastic linear quadratic optimal control problem for state equations of the Itô-SPalabras claves:Itô-Skorokhod integral, Polynomial chaos expansion method, Riccati equations, Stochastic linear quadratic optimal control problem, White noise analysisAutores:Hermann Mena, Levajkovic T., Tuffaha A.Fuentes:scopus