Markov跳变系统网络化状态估计与优化的正系统方法研究

As modern industrial systems are becoming more and more complex and networking, and the requirement of the operation cost is increasing as well, it demands the development of estimation theory facing high real-time performance, fast convergence and strong robustness. Traditional estimation methods apply to achieve the estimation after the system becomes stable, however, system in noise and network environment suffering from uncertainty and randomness may experience long time to be stable or even divergent, being unable to estimate in a real-time manner. Inspired by the idea of positive interval observation, this project will conduct a thorough research on positive system approach for robust networked estimation and optimization of uncertain Markov jump systems. In this project, we will propose delay-dependent positive interval observation methods for Markov jump systems; co-design methods of the Markov transition probability matrix and the interval observer gains for dual switching positive Markov jump systems; modeling method of network characteristics such as the power allocation in network and the network topology based on positive Markov jump systems with time-delays, and positive system methods for network filtering under a power allocation scheme. Finally, from the perspective of cyber-physical systems and positive interval observation systems, the real-time security monitoring method of the hybrid AC/DC power grid will be explored. This project contributes to the study on the crosses and integration of positive systems, networked systems and electrical power systems, etc., and establishing positive system theory targeting robust networked estimation. The results of this project can provide innovative theory guidance and technique support to construct practical systems in a complex operation environment with safe, stable, efficient and economical features.

现代工业系统日趋复杂化和网络化，系统运营对性能的要求越来越高，亟待估计理论面向实时性高、收敛性快和鲁棒性强发展。传统估计方法要求系统达到稳态后才能实现估计，但系统在噪声、网络化环境下的不确定性和随机性，使其稳定周期延长甚至发散，导致无法进行实时估计。受区间观测思想启发，本项目将深入研究不确定Markov跳变系统的网络化鲁棒状态估计与优化的正系统方法，拟提出：Markov跳变系统的时滞依赖的正区间观测方法；双切换正Markov跳变系统的Markov切换概率和观测增益的协同设计方法；网络特征（能量模型和切换拓扑）的时滞正Markov跳变系统建模以及基于能量分配网络化滤波的正系统方法。最后，在物理网络系统和正区间观测系统视角下探索交直流电网安全信息的实时监测方法。项目研究交叉融合正系统、网络化系统和电力系统等领域，建立网络化鲁棒估计的正系统理论，以实现复杂运营环境下系统安全稳定、高效经济运行。

随着实际系统网络化的普及和系统性能要求的增高，融合系统运营约束和网络通讯约束的控制理论研究愈发重要。本项目主要研究在非线性、随机性与不确定等系统约束和通讯时延、数据丢包等网络通讯约束下正系统的稳定性与性能分析，以及网络化分布式正性区间状态估计与控制的新方法，探索解决智能电网和电动汽车领域中网络化引入的一些新问题。.取得的重要成果和科学意义具体如下：（1）关于时滞正Markov跳变线性系统的随机稳定性分析与滤波器/控制器设计，提出了时滞依赖的、Markov转移概率/速率依赖的和指数衰减率依赖的条件。该成果揭示了系统正性、Markov跳变特性和时滞特性与各种随机稳定性之间的依赖关系。（2）提出了随机通讯时延、随机欺骗攻击等网络通讯约束下正性估计误差系统建模与分布式正性区间状态估计方法。该成果解决了网络环境下一些不确定性和随机性导致系统正性难以保证的问题，揭示了网络约束对正系统稳定性与性能的影响，并在数值上实现了智能电网的远程分布式配电实时监测问题的应用。（3）提出了网络诱导时延、随机丢包、网络攻击等网络通讯约束下基于采样数据驱动的比例积分控制、分布式自抗扰控制和模型跟踪控制等新策略。该成果重新评估了不同网络约束对传统控制的影响，并能够解决电动汽车的一些远程控制问题。.本项目的顺利完成在一定程度上推动了信息物理系统和时滞正Markov跳变线性系统的深度交叉融合，形成了具有原始创新的分布式正性区间估计策略和控制方法，并探索了其在智能电网和电动汽车领域中的应用。