ASYMPTOTIC PROBLEMS IN OPTIMAL CONTROL WITH A VANISHING LAGRANGIAN AND UNBOUNDED DATA

MONICA MOTTA; CATERINA SARTORI

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ASYMPTOTIC PROBLEMS IN OPTIMAL CONTROL WITH A VANISHING LAGRANGIAN AND UNBOUNDED DATA

机译：具有消失的拉格朗日和无界数据的最优控制中的渐近问题

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In this paper we give a representation formula for the limit of the finite horizon problem as the horizon becomes infinite, with a nonnegative Lagrangian and unbounded data. It is related to the limit of the discounted infinite horizon problem, as the discount factor goes to zero. We give sufficient conditions to characterize the limit function as unique nonnegative solution of the associated HJB equation. We also briefly discuss the ergodic problem.

机译：在本文中，我们给出了随着非负Lagrangian数据和无界数据，当视界变得无限时有限视界问题极限的表示公式。当贴现因子变为零时，它与无限制无限期问题的极限有关。我们给出了足够的条件来将极限函数表征为相关HJB方程的唯一非负解。我们还将简要讨论遍历问题。

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来源
《Discrete and continuous dynamical systems》 |2015年第9期|4527-4552|共26页
作者
MONICA MOTTA; CATERINA SARTORI;
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作者单位

Dipartimento di Matematica Via Trieste, 63 35121 Padova, Italy;

Dipartimento di Matematica Via Trieste, 63 35121 Padova, Italy;

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正文语种 eng
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关键词
Asymptotic behaviour; optimal control problems with unbounded data; impulsive controls; unbounded viscosity solutions .;

机译：渐近行为;无限数据的最佳控制问题;冲动控制;无限粘度溶液。;

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1. Lagrangian manifolds and asymptotically optimal stabilizing feedback control [J] . McCaffrey D., Banks SP. Systems and Control Letters . 2001,第3期

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2. Bounded-from-below solutions of the Hamilton-Jacobi equation for optimal control problems with exit times: vanishing lagrangians, eikonal equations, and shape-from-shading [J] . Michael Malisoff Nonlinear differential equations and applications: NoDEA . 2004,第1期

机译：具有退出时间的最优控制问题的Hamilton-Jacobi方程的有界解：消失的拉格朗日方程，Eikonal方程和阴影形状
3. Viscosity solutions of the Bellman equation for exit time optimal control problems with vanishing Lagrangians [J] . Malisoff M. SIAM Journal on Control and Optimization . 2002,第5期

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4. Asymptotically consensus tracking control of connected Lagrangian systems with input quantization [C] . Chaoli Wang, Yu Li Chinese Control and Decision Conference . 2020

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5. OPTIMAL LINEAR COMBINATIONS OF CONSISTENT, ASYMPTOTICALLY NORMAL ESTIMATORS (SAMPLE, GROUPED, QUANTILES, DATA, MIXED). [D] . FROM, STEVEN GLEN. 1985

机译：一致，渐近正态估计（样本，分组，量子，数据，混合）的最优线性组合。
6. Addendum: A database of optimal integration times for Lagrangian studies of atmospheric moisture sources and sinks [O] . Raquel Nieto, Luis Gimeno 2021

机译：附录：大气湿度源和水槽拉格朗日研究的最佳集成时间数据库
7. Asymptotic problems in optimal control with a vanishing Lagrangian and unbounded data [O] . Monica Motta, Caterina Sartori 2015

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8. Optimal Linear Combination of Control Variates in the Presence of Asymptotically Negligible Bias. [R] . Glynn, P. W., Iglehart, D. L. 1989

机译：渐近可忽略偏差存在下控制变量的最优线性组合。

ASYMPTOTIC PROBLEMS IN OPTIMAL CONTROL WITH A VANISHING LAGRANGIAN AND UNBOUNDED DATA

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