M. Gugat, M. Schuster, E. Zuazua. The Finite-Time Turnpike Phenomenon for Optimal Control Problems: Stabilization by Non-Smooth Tracking Terms, in “Stabilization of Distributed Parameter Systems: Design Methods and Applications”. Grigory Sklyar Alexander Zuyev Eds., ICIAM 2019 SEMA SIMAI Springer Series 2, p. 17-42. ISSN 2199-3041

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  • In this paper, problems of optimal control are considered where in the objective function, in addition to the control cost, there is a tracking term that measures the distance to a desired stationary state. The tracking term is given by some norm, and therefore it is in general not differentiable. In the optimal control problem, the initial state is prescribed. We assume that the system is either exactly controllable in the classical sense or nodal profile controllable. We show that both for systems that are governed by ordinary differential equations and for infinite-dimensional systems, for example, for boundary control systems governed by the wave equation, under certain assumptions, the optimal system state is steered exactly to the desired state after finite time.

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Metadaten
Author:Martin Gugat, Michael Schuster, Enrique Zuazua
Publisher:Springer International Publishing
Document Type:Article
Language:English
Date of Publication (online):2020/06/12
Date of first Publication:2020/10/02
Release Date:2020/10/02
Volume:SEMA SIMAI Springer Series 2
Article Number:ISSN 2199-3041
Edition:Grigory Sklyar Alexander Zuyev Eds., ICIAM 2019
Page Number:17-42
First Page:17
Last Page:42
Subprojects:C03
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International