报告人：Emmanuel Trélat (法国索邦大学)

日期：2021年03月04日

时间：19:00开始

会议链接https://zoom.us/j/94582600221?pwd=aDc5dlc1NVBNTjdudFVkeHBHdy9tQT09 

Zoom ID：945 8260 0221（密码：4RCniZ）

摘要:The turnpike property was discovered in the 50's by the Nobel prize Samuelson in econometry. It stipulates that the optimal trajectory of an optimal control problem in large time remains essentially close to a steady state, itself being the optimal solution of an associated static optimal control problem. Turnpike phenomena appear in many problems in various fields: mechanics, biology, economics, social behavior, even in sports.
We have established the turnpike property for general nonlinear finite and infinite dimensional optimal control problems, showing that the optimal trajectory is, except at the beginning and the end of the time interval, exponentially close to some (optimal) stationary state, and that this property holds as well for the optimal control and for the adjoint vector coming from the Pontryagin maximum principle. We prove that the exponential turnpike property is due to an hyperbolicity phenomenon which is intrinsic to the symplectic feature of the extremal equations. We infer a simple and efficient numerical method to compute optimal trajectories in that framework, in particular an appropriate variant of the shooting method.
The turnpike property turns out to be ubiquitous and the turnpike set may be more general than a single steady-state, like for instance a periodic trajectory. We also show the property of shape turnpike for PDE models in which a subdomain evolves in time according to some optimization criterion. These works are in collaboration with Gontran Lance, Can Zhang and Enrique Zuazua.

简介:Emmanuel Trélat教授是第28届国际数学家大会45分钟邀请报告人, 巴黎数学科学基金会主任(2015---2019)，2020年起为法国索邦大学Jacques-Louis Lions 实验室负责人。 Emmanuel Trélat的研究专注于有限和无限维的控制理论，次黎曼几何，图像分析，领域优化。 他还是最佳控制数值方法的专家，特别是在航空航天应用中。

个人主页：https://www.ljll.math.upmc.fr/trelat/

联系人：穆春来  周德芹

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