自确定系统的现代最优控制理论建立伊始，人们就尝试研究随机系统的最优控制理论。而在现实中，包括分数维布朗运动等更一般Gauss过程在水文学、经济金融、物理工程和生物数学等方面的研究中具有重要作用，因此研究由一般Gauss过程驱动的随机最优控制系统就显得很有必要。对于这类控制系统因为状态过程通常不再有Markov半群性质，这使得动态规划方法往往不再适用。因此从变分法的角度研究相应的随机最大值原理就成了刻画此类问题的最优控制的主要方法之一。我们在本项目中拟结合Malliavin分析理论和倒向随机微分方程理论研究一般Gauss过程驱动的随机最优控制系统的最优控制所满足的必要条件及在金融与生物数学等领域中的应用；讨论相应伴随方程及广义随机哈密顿系统解的存在惟一性等基本性质。这些问题研究不仅在随机最优控制理论研究方面有一定意义，还能加深我们对各个领域出现的随机系统的了解，增强对不确定现象的认识。

Since the modern optimal control theory to deterministic systems was founded, many researcher try to study the optimal control theory for stochastic optimal control systems. In reality, general Gauss process including fractional Brownian motion play an important role in the fields of hydrology, economic and financial, physical, engineering and biology, so it is very necessary to do further research on the stochastic optimal control system driven by the general Gauss process. By using the dynamic programming principle to derive the HJB equation for the value function is no longer applicable because that the state process for this kind of control system usually has no Markovian semigroup property. So how to obtain the stochastic maximum principle by calculus of variations has become one of the main methods for describing the optimal control of the above mentioned systems. In this project, combing with the theories of Malliavin calculus and backward stochastic differential equations, we investigate the necessary conditions that the optimal control must satisfy for controlled system driven by general Gauss processes such as fractional Brownian motion; The applications of this type of control systems is studied; We also study the existence and uniqueness of the solutions for corresponding adjoint equations and generalized stochastic Hamiltonian systems. To solve these problems in this project will help us deepen the understanding of the phenomenon of uncertainty in real world.