非线性随机系统合作微分博弈的鲁棒Pareto策略研究

由于现代工业和经济的大规模发展，实际系统呈现多决策者、多目标特征，而且系统通常会受到各种不可忽视的外部干扰的影响。针对多决策者、多目标的优化问题，如何运用博弈理论和控制理论的方法发展合作型鲁棒Pareto控制策略，既能兼顾系统的鲁棒性，又能兼顾个体利益和整体利益，是一个亟待解决而困难的科学问题。本项目旨在基于随机非线性鲁棒控制和合作微分博弈理论，深入探索多个主体相互合作情形下的鲁棒Pareto策略问题。首先，结合凸分析理论和参数化方法，得到无外扰Pareto策略的充分/必要条件。其次，通过耦合的HJB方程组解的存在性和多目标系统耗散性理论，分别给出鲁棒Pareto策略的充分条件和必要条件。再次，基于神经网络的策略迭代法给出耦合的HJB方程组数值算法、数值仿真验证。最后，将利用中国石化石油化工科学研究院提供的数据，对项目研究结论验证和完善，为石油加工企业调度作业系统提供理论和算法支持。

Due to large-scale developments of modern industry and economy, practical systems take on the characteristics of multi-decision makers and multi-objectives. Moreover, systems are often affected by kinds of external disturbances that cannot be ignored. For the optimization problem with multi-decision makers and multi-objectives, how to use the methods of game theory and control theory to find the cooperative-type robust Pareto control strategies to balance not only the system robustness, but also the benefits of each individual and all individuals, is an urgent and difficult scientific problem. Based on nonlinear stochastic robust control theory and cooperative differential game theory, this project aims to explore the robust Pareto strategy deeply in the case that multi-players cooperate their actions with each other. Firstly, combining the convex analysis theory and the parameterized method, sufficient/necessary conditions for the existence of the Pareto strategy have been obtained for the system without external disturbances. Secondly, based on the existence of the solution of the coupled HJB equations and the dissipative theory of multi-objective systems, we will present the sufficient and necessary conditions of robust Pareto control strategies, respectively. Thirdly, numerical algorithms of coupled HJB equations have been given by a policy iteration method based on neural network. Numerical simulation examples are presented to verify the effectiveness of the developed theory. Finally, we will use the data provided by the Sinopec Research Institute of Petroleum Processing to verify and perfect the obtained theory, which can also provide theoretical and algorithmic support for the scheduling operating system of petroleum processing enterprises.