Exponential sensitivity and turnpike analysis for linear quadratic optimal control of general evolution equations

Title data

Grüne, Lars ; Schaller, Manuel ; Schiela, Anton: Exponential sensitivity and turnpike analysis for linear quadratic optimal control of general evolution equations.
Department of Mathematics, University of Bayreuth
Bayreuth
,
2018
. - 22 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 linear quadratic optimal control problems governed by general evolution equations with bounded or admissible control operator. We show, that if the problem is stabilizable and detectable, the solution of the extremal equation can be bounded by the right-hand side including initial data with the bound being independent of the time horizon. Consequently, the influence of perturbations of the extremal equations decays exponentially in time. This property can for example be used to construct efficient space and time discretizations for a Model Predictive Control scheme. Furthermore, a turnpike property for unbounded but admissible control of general semigroups can be deduced.

Further data

Item Type:

Preprint, postprint, working paper, discussion paper

Keywords:

Sensitivity Analysis; Turnpike Property; Model Predictive Control