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.
Authors with CRIS profile
Enrique Zuazua Iriondo
Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)
Involved external institutions
Japan (JP)How to cite
APA:
Sakamoto, N., & Zuazua Iriondo, E. (2021). The turnpike property in nonlinear optimal control – A geometric approach. Automatica, 134, 109939. https://dx.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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