The turnpike property in nonlinear optimal control-A geometric approach

Sakamoto N, Zuazua Iriondo E (2021)


Publication Type: Journal article

Publication year: 2021

Journal

Book Volume: 134

DOI: 10.1016/j.automatica.2021.109939

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 behavior to occur. The approach taken is geometric and gives insights for the behaviors of controlled trajectories as well as links between the turnpike property 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. (C) 2021 Elsevier Ltd. All rights reserved.

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APA:

Sakamoto, N., & Zuazua Iriondo, E. (2021). The turnpike property in nonlinear optimal control-A geometric approach. Automatica, 134. 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).

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