An Error Estimate for Symplectic Euler Approximation of Optimal Control Problems
Journal article, 2015

This work focuses on numerical solutions of optimal control problems. A time discretization error representation is derived for the approximation of the associated value function. It concerns symplectic Euler solutions of the Hamiltonian system connected with the optimal control problem. The error representation has a leading-order term consisting of an error density that is computable from symplectic Euler solutions. Under an assumption of the pathwise convergence of the approximate dual function as the maximum time step goes to zero, we prove that the remainder is of higher order than the leading-error density part in the error representation. With the error representation, it is possible to perform adaptive time stepping. We apply an adaptive algorithm originally developed for ordinary differential equations. The performance is illustrated by numerical tests.

adaptivity

error control

optimal control

error estimates

Author

J. Karlsson

King Abdullah University of Science and Technology (KAUST)

Dynamore Nordic Ab

Stig Larsson

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

M. Sandberg

Royal Institute of Technology (KTH)

A. Szepessy

Royal Institute of Technology (KTH)

R. Tempone

King Abdullah University of Science and Technology (KAUST)

SIAM Journal of Scientific Computing

1064-8275 (ISSN) 1095-7197 (eISSN)

Vol. 37 2 A946-A969

Subject Categories

Computational Mathematics

DOI

10.1137/140959481

More information

Latest update

9/6/2018 1