Optimal Control for ODEs and PDEs: The Turnpike Phenomenon

Gugat M, Zuazua Iriondo E, Schuster M (2022)

Publication Language: English

Publication Type: Conference contribution, Abstract of lecture

Publication year: 2022

Conference Proceedings Title: Extended Abstracts of the 65th Joint Conference on Automatic Control

Event location: Utsunomiya JP

Open Access Link: https://www.jsme.or.jp/conference/rengo65/

Abstract

The turnpike phenomenon for dynamic optimal control problems provide insights about the relation between the dynamic optimal control and the solution of the corresponding static optimal control problem. In this talk we give an overview about different turnpike structures for optimal control problems with ordinary differential equations (ODEs) and partial differential equations (PDEs). 

For optimal control problems with ODEs an exponential turnpike inequality can be shown by basic control theory. These results can be extended to an integral turnpike inequality for optimal control problems with linear hyperbolic systems. For an optimal control problem with non differential tracking term in the objective function, that is exactly controllable, we can show under certain assumptions that the optimal system state is steered exactly to the desired state after finite time. Further we consider an optimal control problem for a hyperbolic system with random boundary data and we show the existence of optimal controls. A turnpike property for hyperbolic systems with random boundary data can be shown numerically.

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 Iriondo, E., & Schuster, M. (2022). Optimal Control for ODEs and PDEs: The Turnpike Phenomenon. Paper presentation at 65th Joint Conference on Automatic Control, Utsunomiya, JP.

MLA:

Gugat, Martin, Enrique Zuazua Iriondo, and Michael Schuster. "Optimal Control for ODEs and PDEs: The Turnpike Phenomenon." Presented at 65th Joint Conference on Automatic Control, Utsunomiya 2022.

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