离散时间随机系统的二阶必要最优条件

Teng Song, Yong Yao
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摘要

本文论述了弱化凸性假设下离散时间随机最优控制问题的二阶必要最优性条件。利用控制的一种特殊变化,并凭借一个新的离散-时间后向随机方程,我们以全局随机最大原则的形式建立了一个更具一般性和建设性的一阶必要最优条件。此外,通过引入新的离散时间后向随机矩阵方程,我们还推导出了奇异控制的二阶多点必要最优条件,涵盖并改进了离散时间随机系统的经典二阶必要最优条件。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Second-order necessary optimality conditions for discrete-time stochastic systems

Second-order necessary optimality conditions for discrete-time stochastic systems
This paper deals with the second-order necessary optimality conditions for discrete-time stochastic optimal control problems under weakened convexity assumptions. Using a special variation of the control, and by virtue of a new discrete-time backward stochastic equation, we establish a more general and constructive first-order necessary optimality condition in the form of a global stochastic maximum principle. Moreover, by introducing a new discrete-time backward stochastic matrix equation, the second-order multipoint necessary optimality conditions of singular controls are derived, which covers and improves the classical second-order necessary optimality conditions of discrete-time stochastic systems.
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