Gugat M, Schuster M, Zuazua Iriondo E (2021)
Publication Type: Book chapter / Article in edited volumes
Publication year: 2021
Publisher: Springer Science and Business Media Deutschland GmbH
Edited Volumes: Stabilization of Distributed Parameter Systems: Design Methods and Applications
Series: SEMA SIMAI Springer Series
Book Volume: 2
Pages Range: 17-41
ISBN: 978-3-030-61742-4
DOI: 10.1007/978-3-030-61742-4_2
Open Access Link: https://arxiv.org/abs/2006.07051
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.
APA:
Gugat, M., Schuster, M., & Zuazua Iriondo, E. (2021). The Finite-Time Turnpike Phenomenon for Optimal Control Problems: Stabilization by Non-smooth Tracking Terms. In Grigory Sklyar, Alexander Zuyev (Eds.), Stabilization of Distributed Parameter Systems: Design Methods and Applications. (pp. 17-41). Springer Science and Business Media Deutschland GmbH.
MLA:
Gugat, Martin, Michael Schuster, and Enrique Zuazua Iriondo. "The Finite-Time Turnpike Phenomenon for Optimal Control Problems: Stabilization by Non-smooth Tracking Terms." Stabilization of Distributed Parameter Systems: Design Methods and Applications. Ed. Grigory Sklyar, Alexander Zuyev, Springer Science and Business Media Deutschland GmbH, 2021. 17-41.
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