The turnpike property in nonlinear optimal control—A geometric approach

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 ob...

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Bibliographic Details
Published inAutomatica (Oxford) Vol. 134; p. 109939
Main Authors Sakamoto, Noboru, Zuazua, Enrique
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.12.2021
Subjects
Nonlinear system
Optimal control
Turnpike
Optimal control
Nonlinear system
Turnpike
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Summary: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.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2021.109939