Numerical solution of the finite horizon stochastic linear quadratic control problem

Damm, Tobias; Mena, Hermann; Stillfjord, Tony

doi:10.1002/nla.2091

Cited by 14 publications

(17 citation statements)

References 51 publications

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“…Following [11,12], we approximate the integral by a quadrature formula with weights w k and nodes τ k and obtain a low-rank approximation P 1 P T 1 to P (h) of the form P 1 = e hA P 0 , hw 1 e τ1A P 0 , hw 2 e τ2A P 0 , . .…”

Section: Numerical Methods For the Mean And The Covariancementioning

confidence: 99%

“…As in [12], we apply splitting methods and compose equation (16) into the two parts F 1 and F 2 , where The idea is to compute the subproblemsṖ = F k P which is cheaper to compute than the full problem. Let T k (t)P (0) be the solution of the subprobleṁ P = F k P , then the Strang splitting is given by…”

Section: Numerical Methods For the Mean And The Covariancementioning

confidence: 99%

“…We again obtain a low-rank approximation P 1 P T 1 of P (h). A detailed description of this splitting scheme is given in [11,12]. On the other hand, it is also possible to apply an ordinary differential equation solver in matrix setting and then to solve the resulting algebraic generalized Lyapunov equation by numerical solvers like the ones proposed in [15,17].…”

Section: Numerical Methods For the Mean And The Covariancementioning

confidence: 99%

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An efficient SPDE approach for El Niño

Mena

Pfurtscheller

2019

Applied Mathematics and Computation

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We consider the numerical approximation of stochastic partial differential equations (SPDEs) based models for a quasi-periodic climate pattern in the tropical Pacific Ocean known as El Niño phenomenon. We show that for these models the mean and the covariance are given by a deterministic partial differential equation and by an operator differential equation, respectively. In this context we provide a numerical framework to approximate these parameters directly. We compare this method to stochastic differential equations and SPDEs based models from the literature solved by Taylor methods and stochastic Galerkin methods, respectively. Numerical results for different scenarios taking as a reference measured data of the years 2014 and 2015 (last Niño event) validate the efficiency of our approach.

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Section: Numerical Methods For the Mean And The Covariancementioning

confidence: 99%

Section: Numerical Methods For the Mean And The Covariancementioning

confidence: 99%

Section: Numerical Methods For the Mean And The Covariancementioning

confidence: 99%

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An efficient SPDE approach for El Niño

Mena

Pfurtscheller

2019

Applied Mathematics and Computation

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“…The first two subproblems are handled as before, whereas we approximate T 4 (h)(P ) by the midpoint rule, analogously to what is done in [20]:…”

Section: 3mentioning

confidence: 99%

GPU acceleration of splitting schemes applied to differential matrix equations

2019

Self Cite

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We consider differential Lyapunov and Riccati equations, and generalized versions thereof. Such equations arise in many different areas and are especially important within the field of optimal control. In order to approximate their solution, one may use several different kinds of numerical methods. Of these, splitting schemes are often a very competitive choice. In this article, we investigate the use of graphical processing units (GPUs) to parallelize such schemes and thereby further increase their effectiveness. According to our numerical experiments, large speed-ups are often observed for sufficiently large matrices. We also provide a comparison between different splitting strategies, demonstrating that splitting the equations into a moderate number of subproblems is generally optimal.

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“…In Algorithm 1 we summarize the above proposed Lie splitting for the solution of (10). Note that the flows of all these substeps can be computed exactly.…”

Section: A Low-rank Split-step Integratormentioning

confidence: 99%

Numerical low-rank approximation of matrix differential equations

Mena

Ostermann

Pfurtscheller

et al. 2018

Journal of Computational and Applied Mathematics

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The efficient numerical integration of large-scale matrix differential equations is a topical problem in numerical analysis and of great importance in many applications. Standard numerical methods applied to such problems require an unduly amount of computing time and memory, in general. Based on a dynamical lowrank approximation of the solution, a new splitting integrator is proposed for a quite general class of stiff matrix differential equations. This class comprises differential Lyapunov and differential Riccati equations that arise from spatial discretizations of partial differential equations. The proposed integrator handles stiffness in an efficient way, and it preserves the symmetry and positive semidefiniteness of solutions of differential Lyapunov equations. Numerical examples that illustrate the benefits of this new method are given. In particular, numerical results for the efficient simulation of the weather phenomenon El Niño are presented.

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Numerical solution of the finite horizon stochastic linear quadratic control problem

Cited by 14 publications

References 51 publications

An efficient SPDE approach for El Niño

An efficient SPDE approach for El Niño

GPU acceleration of splitting schemes applied to differential matrix equations

Numerical low-rank approximation of matrix differential equations

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