Exponential sensitivity analysis for Model Predictive Control of PDEs

Titelangaben

Grüne, Lars ; Schaller, Manuel ; Schiela, Anton:
Exponential sensitivity analysis for Model Predictive Control of PDEs.
Department of Mathematics, University of Bayreuth
Bayreuth , 2020 . - 4 S.

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Abstract

Model Predictive Control (MPC) is a control method in which the solution of optimal control problems on infinite or indefinitely long horizons is split up into the successive solution of optimal control problems on relatively short finite time horizons. Only a first part of this solution with given length is implemented as a control for the longer, possibly infinite horizon. Motivated by this application, we analyze the propagation of discretization errors in the context of optimal control of abstract evolution equations in infinite dimensional spaces. Using a particular stability property, one can show that indeed the error decays exponentially in time, leading to very efficient time and space discretization schemes for MPC. In particular, one can rigorously explain the behavior of goal oriented error estimation algorithms used in this context. Furthermore, an exponential turnpike theorem will be derived. We give particular applications of this abstract theory to admissible control of hyperbolic equations, nonautonomous and semilinear parabolic equations. Eventually, we present several numerical examples illustrating the theoretical findings.