Efficient Model Predictive Control for Parabolic PDEs with Goal Oriented Error Estimation

Understand

We show how a posteriori goal oriented error estimation can be used to efficiently solve the subproblems occurring in a Model Predictive Control (MPC) algorithm.

• In MPC, only an initial part of a computed solution is implemented as a feedback, which motivates grid refinement particularly tailored to this context.
• To this end, we present a truncated cost functional as objective for goal oriented adaptivity and prove under stabilizability assumptions that error indicators decay exponentially outside the support of this quantity.
• This leads to very efficient time and space discretizations for MPC, which we will illustrate by means of various numerical examples.