In this paper, the fuzzy variational problem and fuzzy optimal control problem are considered. The granular Euler–Lagrange condition for the fuzzy variational problem and necessary conditions of Pontryagin type for fixed and free final state fuzzy optimal control problem are derived based on the concepts of horizontal membership function (HMF) and granular differentiability with the calculus of variations. Further, based on the proposed solution method, the solutions of fuzzy optimal control problem, i.e., optimal fuzzy control, and corresponding optimal fuzzy state are always fuzzy functions. Finally, the proposed algorithm used to summarize the main steps of solving the fuzzy variational problem and fuzzy optimal control problem numerically using He's variational iteration method (VIM).

本文考虑了模糊变分问题和模糊最优控制问题。基于水平隶属函数(HMF)和粒微可微性的概念，利用变分演算，推导出模糊变分问题的粒状欧拉-拉格朗日条件和固定和自由终态模糊最优控制问题的庞特里亚金型必要条件。进一步地，基于所提出的求解方法，模糊最优控制问题的解，即最优模糊控制，以及相应的最优模糊状态总是模糊函数。最后，所提出的算法利用He的变分迭代法(VIM)对模糊变分问题和模糊最优控制问题进行数值求解的主要步骤进行了总结。