本项目旨在研究一般非线性离散随机系统的Pareto优化及其应用。首先，离散随机系统是描述航空航天、基因调控网络、 网络控制、金融投资等领域许多重要问题的理想的数学模型。 其次，Pareto优化是一种重要的合作型博弈，在经济管理、无线通讯、信号处理等领域发挥重要的作用。可以发现：迄今为止，大多数的工作都集中在微分博弈和非合作博弈，然而随机差分Pareto优化由于数学上的高难度，目前研究成果极少。本项目首先研究一般非线性离散随机系统的多目标Pareto优化问题。 通过发展更一般离散随机系统的最大值原理和验证定理，给出Pareto有效策略存在的充分/必要条件。特别地， 对于仿射非线性离散随机系统，我们拟利用模糊线性化方法给出Pareto有效策略设计的凸优化算法。作为应用，我们将所发展的理论应用到金融投资、非线性离散随机系统的多目标H2/H∞滤波器设计。

This project aims to study the Pareto optimization of general nonlinear discrete-time stochastic systems with its applications. Firstly, discrete-time stochastic systems are ideal models in describing many important issues arising from the fields of aeronautics and astronautics, genetic regulatory networks, network controls, and financial investments, etc.. Secondly, the Pareto optimization is an important cooperative game, which plays crucial roles in economic management, wireless communication, and signal processing, etc.. It can be found that, up to now, most existing works are forcused on differential game and non-cooperative game， while there are few works on stochastic difference Pareto optimization due to that it is more complicated in mathematics. This project will first study multiobjective Pareto optimization of general nonlinear discrete-time stochastic systems. By developing more general discrete-time stochastic maximum principle and verification theorem, we will present sufficient/necessary conditions for the existence of Pareto efficient strategies. In particular, for affine nonlinear discrete-time stochastic systems, we apply the fuzzy linearization method to give a convex optimization method in designing the Pareto efficient strategies. As applications, we will apply the developed theories to financial investment and multiobjective H2/H∞ filtering design of nonlinear discrete-time stochastic systems.