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Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. Efficient Higher Order Time Discretization Schemes For Hamilton–Jacobi–Bellman Equations Based On Diagonally Implicit Symplectic Runge–Kutta Methods
 Kalise, D.: HamiltonJacobiBellman equations : Numerical methods and applications in optimal control Berlin: De Gruyter, 2018 (Radon series on computational and applied mathematics 21) ISBN: 9783110543599 ISBN: 9783110542714 ISBN: 9783110542639 pp.97128 

 English 
 Book Article 
 Fraunhofer SCAI () 
Abstract
We consider a semiLagrangian approach for the computation of the value function of a HamiltonJacobiBellman equation. This problem arises when one solves optimal feedback control problems for evolutionary partial differential equations. A time discretization with RungeKutta methods leads in general to a complexity of the optimization problem for the control which is exponential in the number of stages of the time scheme. Motivated by this, we introduce a time discretization based on RungeKutta composition methods, which achieves higher order approximation with respect to time, but where the overall optimization costs increase only linearly with respect to the number of stages of the employed RungeKutta method. In numerical tests we can empirically confirm an approximately linear complexity with respect to the number of stages. The presented algorithm is in particular of interest for those optimal control problems which do involve a costly minimization over the control set