Hamiltonian based a posteriori error estimation for Hamilton-Jacobi-Bellman equations

Titelangaben

Grüne, Lars ; Dower, Peter:
Hamiltonian based a posteriori error estimation for Hamilton-Jacobi-Bellman equations.
In: Proceedings of the 23rd International Symposium on Mathematical Theory of Networks and Systems. - Hong Kong , 2018 . - S. 372-374

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Abstract

In this extended abstract we present a method for the a posteriori error estimation of the numerical solution to Hamilton-Jacobi-Bellman PDEs related to infinite horizon optimal control problems. The method uses the residual of the Hamiltonian, i.e., it checks how good the computed numerical solution satisfies the PDE and computes the difference between the numerical and the exact solution from this mismatch. We present results both for discounted and for undiscounted problems, which require different mathematical techniques. For discounted problems, an inherent contraction property can be used while for undiscounted problems an asymptotic stability property of the optimally controlled system is exploited.