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• W2964087020 abstract "Turnpike properties have been established long time ago in finite-dimensional optimal control problems arising in econometry. They refer to the fact that, under quite general assumptions, the optimal solutions of a given optimal control problem settled in large time consist approximately of three pieces, the first and the last of which being transient short-time arcs, and the middle piece being a long-time arc staying exponentially close to the optimal steady-state solution of an associated static optimal control problem. We provide in this paper a general version of a turnpike theorem, valuable for nonlinear dynamics without any specific assumption, and for very general terminal conditions. Not only the optimal trajectory is shown to remain exponentially close to a steady-state, but also the corresponding adjoint vector of the Pontryagin maximum principle. The exponential closedness is quantified with the use of appropriate normal forms of Riccati equations. We show then how the property on the adjoint vector can be adequately used in order to initialize successfully a numerical direct method, or a shooting method. In particular, we provide an appropriate variant of the usual shooting method in which we initialize the adjoint vector, not at the initial time, but at the middle of the trajectory." @default.
• W2964087020 created "2019-07-30" @default.
• W2964087020 creator A5088702266 @default.
• W2964087020 creator A5089339704 @default.
• W2964087020 date "2015-01-01" @default.
• W2964087020 modified "2023-10-06" @default.
• W2964087020 title "The turnpike property in finite-dimensional nonlinear optimal control" @default.
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• W2964087020 hasPublicationYear "2015" @default.
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