The turnpike property in nonlinear optimal control – A geometric approach

Sakamoto N, Zuazua Iriondo E (2021)


Publication Language: English

Publication Status: Published

Publication Type: Journal article, Original article

Future Publication Type: Journal article

Publication year: 2021

Journal

Publisher: Automatica

Book Volume: 134

Pages Range: 109939

URI: https://dcn.nat.fau.eu/wp-content/uploads/Turnpike_for_Automatica.pdf

DOI: 10.1016/j.automatica.2021.109939

Open Access Link: https://dcn.nat.fau.eu/wp-content/uploads/Turnpike_for_Automatica.pdf

Abstract

This paper presents, using dynamical system theory, a framework for investigating the turnpike property in nonlinear optimal control. First, it is shown that a turnpike-like property appears in general dynamical systems with hyperbolic equilibrium and then, apply it to optimal control problems to obtain sufficient conditions for the turnpike to occurs. The approach taken is geometric and gives insights for the behaviors of controlled trajectories as well as links between the turnpike and stability and/or stabilizability in nonlinear control theory. It also allows us to find simpler proofs for existing results on the turnpike properties. Attempts to remove smallness restrictions for initial and target states are also discussed based on the geometry of (un)stable manifolds and a recent result on exponential stabilizability of nonlinear control systems obtained by one of the authors.

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How to cite

APA:

Sakamoto, N., & Zuazua Iriondo, E. (2021). The turnpike property in nonlinear optimal control – A geometric approach. Automatica, 134, 109939. https://doi.org/10.1016/j.automatica.2021.109939

MLA:

Sakamoto, Noboru, and Enrique Zuazua Iriondo. "The turnpike property in nonlinear optimal control – A geometric approach." Automatica 134 (2021): 109939.

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