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

Titelangaben

Grüne, Lars ; Schaller, Manuel ; Schiela, Anton:
Exponential sensitivity and turnpike analysis for linear quadratic optimal control of general evolution equations.
In: Journal of Differential Equations. Bd. 268 (2020) Heft 12 . - S. 7311-7341.
ISSN 1090-2732
DOI: https://doi.org/10.1016/j.jde.2019.11.064

Volltext

Link zum Volltext (externe URL):

Weitere URLs

Angaben zu Projekten

Abstract

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.