The turnpike property in nonlinear optimal control—A geometric approach. (December 2021)

• Record Type: Journal Article
• Authors: Sakamoto, Noboru; Zuazua, Enrique
• Is Part Of: Automatica. Volume 134(2021)
• Publication Date: 2021-12
• Subjects: Optimal control -- Nonlinear system -- Turnpike; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2021.109939
• Languages: English
• ISSNs: 0005-1098

Abstract

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.