Abstract nonlinear sensitivity and turnpike analysis and an application to semilinear parabolic PDEs

Title data

Grüne, Lars ; Schaller, Manuel ; Schiela, Anton: Abstract nonlinear sensitivity and turnpike analysis and an application to semilinear parabolic PDEs.
Bayreuth
,
2020
. - 29 p.

Official URL:

Project information

Project title:

Project's official title

Project's id

Specialized Adaptive Algorithms for Model Predictive Control of PDEs

GR 1569/17-1

Specialized Adaptive Algorithms for Model Predictive Control of PDEs

SCHI 1379/5-1

Project financing:

Deutsche Forschungsgemeinschaft

Abstract in another language

We analyze the sensitivity of the extremal equations that arise from the first order necessary optimality conditions of nonlinear optimal control problems with respect to perturbations of the dynamics and of the initial data. To this end, we present an abstract implicit function approach with scaled spaces. We will apply this abstract approach to problems governed by semilinear PDEs. In that context, we prove an exponential turnpike result and show that perturbations of the extremal equation's dynamics, e.g., discretization errors decay exponentially in time. The latter can be used for very efficient discretization schemes in a Model Predictive Controller, where only a part of the solution needs to be computed accurately. We showcase the theoretical results by means of two examples with a nonlinear heat equation on a two-dimensional domain.

Further data

Item Type:

Preprint, postprint

Keywords:

Nonlinear Optimal Control; Sensitivity Analysis; Turnpike Property; Model Predictive Control