Turnpike in optimal shape design

Lance G, Trelat E, Zuazua E (2019)

Publication Type: Conference contribution

Publication year: 2019

Journal

IFAC-PapersOnLine International Federation of Automatic Control

Publisher: Elsevier B.V.

Book Volume: 52

Pages Range: 496-501

Conference Proceedings Title: IFAC-PapersOnLine

Event location: Vienna AT

DOI: 10.1016/j.ifacol.2019.12.010

Abstract

We investigate the turnpike problem in optimal control, in the context of time-evolving shapes. We focus here on the heat equation model where the shape acts as a source term, and we search the optimal time-varying shape, minimizing a quadratic criterion. We first establish existence of optimal solutions under some appropriate sufficient conditions. We provide necessary conditions for optimality in terms of usual adjoint equations and then, thanks to strict dissipativity properties, we prove that state and adjoint satisfy a measure-turnpike property, meaning that the extremal time-varying solution remains essentially close to an optimal solution of an associated static problem. We illustrate the turnpike phenomenon in shape design with several numerical simulations.

Authors with CRIS profile

Enrique Zuazua Iriondo

Involved external institutions

University of Paris 7 - Denis Diderot / Université Paris VII Denis Diderot FR France (FR) University of Deusto / Universidad de Deusto ES Spain (ES)

How to cite

APA:

Lance, G., Trelat, E., & Zuazua, E. (2019). Turnpike in optimal shape design. In Lukasz Jadachowski (Eds.), IFAC-PapersOnLine (pp. 496-501). Vienna, AT: Elsevier B.V..

MLA:

Lance, G., Emmanuel Trelat, and Enrique Zuazua. "Turnpike in optimal shape design." Proceedings of the 11th IFAC Symposium on Nonlinear Control Systems, NOLCOS 2019, Vienna Ed. Lukasz Jadachowski, Elsevier B.V., 2019. 496-501.

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