Markov跳变随机系统的多目标鲁棒Pareto控制与权重优化研究

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，Markov跳变系统可建模为多个子系统，能够更加精确的解决某些带有模态突变性质的实际问题。如何运用数学理论中的多目标优化方法和控制理论的合作控制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Markov跳变随机多目标优化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，结合凸分析理论和动态规划方法，得到鲁棒Pareto策略的充分/必要条件。其次，通过耦合的Riccati方程和广义Lyapunov方程，结合线性二次最优控制理论，给出多目标性能指标非标准情形的鲁棒Pareto策略存在充分条件和必要条件。最后，基于Nash谈判解和K-S谈判解理论探究Pareto解的最优权重分配方法。

Due to the large-scale development of modern industry and economy, the actual system presents the characteristics of multiple decision makers and multiple objectives. The Markov jump system can be modeled as multiple subsystems, which can solve some practical problems with modal mutation. How to develop cooperative robust Pareto control strategy by using the methods of multi-objective optimization theory and cooperative control theory, which can not only take into account the robustness of the system, but also take into account the individual interests and the overall interests, is an urgent and difficult scientific problem. This project aims to deeply explore the problem of robust Pareto strategy in the case of multiple players cooperation based on Markov jump stochastic robust control and cooperative differential game theory. Firstly, the sufficient and necessary conditions of robust Pareto strategy are obtained by combining the convex analysis theory and dynamic programming method. Secondly, through the coupled Riccati equation and the generalized Lyapunov equation, combined with the linear quadratic optimal control theory, the sufficient and necessary conditions for the existence of robust Pareto strategy in the case of nonstandard multiple objectives performance indicators are given.Finally, the optimal weight assignment method of the Pareto solution is explored based on Nash negotiation solution theory and K-S negotiation solution theory.