The Finite-Time Turnpike Phenomenonfor Optimal Control Problems:Stabilization by Non-smooth TrackingTerms

Gugat M, Zuazua E, Schuster M (2021)

Publication Language: English

Publication Type: Book chapter / Article in edited volumes

Publication year: 2021

Publisher: Springer Nature Switzerland AG.The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Edited Volumes: Stabilization of Distributed Parameter Systems: Design Methods and Applications

Series: SEMA SIMAI Springer SeriesICIAM 2019 SEMA SIMAI Springer Series

City/Town: 6330 Cham, Switzerland

Book Volume: 2

Pages Range: 17-41

DOI: 10.1007/978-3-030-61742-4

Abstract

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.

Authors with CRIS profile

Martin Gugat Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur) Enrique Zuazua Iriondo Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur) Michael Schuster Sonderforschungsbereich/Transregio 154: Mathematische Modellierung, Simulation und Optimierung am Beispiel von Gasnetzwerken

How to cite

APA:

Gugat, M., Zuazua, E., & Schuster, M. (2021). The Finite-Time Turnpike Phenomenonfor Optimal Control Problems:Stabilization by Non-smooth TrackingTerms. In Grigory Sklyar, Alexander Zuyev (Eds.), Stabilization of Distributed Parameter Systems: Design Methods and Applications. (pp. 17-41). 6330 Cham, Switzerland: Springer Nature Switzerland AG.The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland.

MLA:

Gugat, Martin, Enrique Zuazua, and Michael Schuster. "The Finite-Time Turnpike Phenomenonfor Optimal Control Problems:Stabilization by Non-smooth TrackingTerms." Stabilization of Distributed Parameter Systems: Design Methods and Applications. Ed. Grigory Sklyar, Alexander Zuyev, 6330 Cham, Switzerland: Springer Nature Switzerland AG.The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland, 2021. 17-41.

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