Abstract

In this article, we study the stochastic fractional optimal control problem for a system governed by a class of non-instantaneous impulsive stochastic fractional differential equation in the infinite-dimensional spaces. We utilize the fractional calculus, stochastic analysis theory and a suitable fixed point approach to present the solvability of the stochastic fractional system. Then, the existence of optimal state-control pairs of the Lagrange problem is derived without uniqueness of solutions of the stochastic system. Finally, the main results are validated with the aid of an example.

中文翻译：

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q ∈ (1,2) 阶非瞬时脉冲随机分数阶微分方程的可解性和最优控制

摘要

在本文中，我们研究了无限维空间中由一类非瞬时脉冲随机分数阶微分方程控制的系统的随机分数优化控制问题。我们利用分数阶微积分、随机分析理论和合适的不动点方法来展示随机分数系统的可解性。然后，在没有随机系统解的唯一性的情况下，导出了拉格朗日问题的最优状态-控制对的存在性。最后，通过实例验证了主要结果。