神经网络理论在微分对策问题中的应用研究

In this project, Neural networks combined with other artificial intelligence and learning control technique are used to study the problem of differential games. A kink of dynamic neural networks is proposed to model the differential games system. Some performances for the dynamic neural networks are addressed, such as controllability and observability, separation principle of learning and control. A hybrid artificial intelligent technique is developed to optimize differential games. The neural networks combined with the theory of multilayer semantic control are introduced to modeling the problem of differential game, which changes the optimization of differential game on two sides into the optimization on one side. And also, the application of the reinforcement learning with neural networks in missile differential game guidance is investigated. The relations between foundational elements of reinforcement learning and differential game are developed. The value function approximation of reinforcement learning with neural networks is studied, and the learning algorithms using modular neural networks to approximate the value function is emphatically analyzed, which decomposes the state space automatically and increases the generalizing ability of the neural networks. A robust controller is synthesized using neural networks. The optimization of robust performance is changed into the minmax problem of differential games. The hybrid adjoint-BP technique with optimal control and backpropagation neural networks is developed to solve the two point boundary value problem of differential games. And last, an adaptive critic structure consisting of two control neural networks and a co-state neural network is constructed based on the two point boundary value problem of differential games．The output of co-state network is used to correct the output of the control networks，which can solve the two point boundary value problem automatically. The above results develop the direct quantitative relations between optimal control and neural networks, which changes the problem of complex optimization into one of neural networks learning. The above results have provided some new methods for the application of differentiall game theory in practice.

本项目对神经网络理论解决微分对策问题的机理进行了研究。首次提出用动态神经网络对微对策问题建模并用非动态神经网络设计最优控制策略的理论和方法；提出并研究用神经网络语义控制理论解决微分对策问题的技术途径。研究神经网络和再励学习解决复杂微分对策的新方法。本课题将为困扰多年的微分对策理论工程应用问题提供行之有效的解决方法。