Title data
Grüne, Lars ; Dower, Peter:
Hamiltonian based a posteriori error estimation for HamiltonJacobiBellman equations.
Bayreuth ; Melbourne
,
2018
.  3 S.


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Project financing: 
Deutsche Forschungsgemeinschaft Model predictive PDE control for energy efficient building operation: Economic model predictive control and time varying systems 
Abstract
In this extended abstract we present a method for the a posteriori error estimation of the numerical solution to HamiltonJacobiBellman 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.