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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:scopusFourier-splitting method for solving hyperbolic LQR problems
ArticleAbstract: We consider the numerical approximation to linear quadratic regulator problems for hyperbolic partiaPalabras claves:Fourier method, Hyperbolic LQR problem, Numerical solution, Operator splitting method, Optimal feedback controlAutores:Csomós P., Hermann MenaFuentes:scopusGPU acceleration of splitting schemes applied to differential matrix equations
ArticleAbstract: We consider differential Lyapunov and Riccati equations, and generalized versions thereof. Such equaPalabras claves:Differential Lyapunov equations, Differential Riccati equations, GPU acceleration, large scale, Splitting schemesAutores:Hermann Mena, Lena Maria Pfurtscheller, Stillfjord T.Fuentes:scopusGeneralized Operators of Malliavin Calculus
Book PartAbstract: In this chapter we extend Malliavin calculus from the classical finite variance setting to generalizPalabras claves:Autores:Hermann Mena, Levajkovic T.Fuentes:scopusEquations Involving Mallivin Calculus Operators
Book PartAbstract: This chapter is devoted to the study of several classes of stochastic equations involving generalizePalabras claves:Autores:Hermann Mena, Levajkovic T.Fuentes:scopusEquations involving malliavin derivative: A chaos expansion approach
Book PartAbstract: We study equations involving the Malliavin derivative operator and the Wick product with a GaussianPalabras claves:Chaos expansion, Galerkin method, Generalized stochastic process, Malliavin derivative, Stochastic differential equation, Wick productAutores:Hermann Mena, Levajkovic T.Fuentes:scopusInnovative integrators for computing the optimal state in LQR problems
Conference ObjectAbstract: We consider the numerical approximation of linear quadratic optimal control problems for partial difPalabras claves:Abstract LQR problems, Convergence Analysis, Exponential integrators, Operator splitting procedures, Optimal ControlAutores:Csomós P., Hermann MenaFuentes:scopusSolving sparse differential riccati equations on hybrid CPU-GPU platforms
Conference ObjectAbstract: The numerical treatment of the linear-quadratic optimal control problem requires the solution of RicPalabras claves:Differential Riccati equation (DRE), feedback control, Implicit Euler, Linearly implicit Euler, LQRAutores:Benner P., Dufrechou E., Ezzatti P., Hermann Mena, Quintana-Ortí E.S., Remón A.Fuentes:scopus