网络化随机脉冲耦合系统的稳定性分析和控制

There are still a lot of problems to deal with for the stability analysis and control of stochastic impulsive coupled systems on networks (SICSNs) . We will employ stochastic differential equation theroy, impulsive differential equation theroy, dynamic system theroy and graph theroy to dissect the modelling, analysis and control for SICSNs, which is a very important type of complex systems, because in practice, many complex phenomena can be depicted and explained by SICSNs. The contents include: (1) Set up SICSN models based on directed graph theory. (2) Discuss stability of SICSNs (including stochastic stability, p-moment stability, input-to-state stability, stablity in partial variables and so on) by exploiting Kirchhoff’s matrix tree theorem and the second Lyapunov method, and some other dynamical properties, such as ergodicity, periodicity and so on. Some criteria related to the topology structure of SICSNs will be presented. (3) Investigate the stabilization and synchronization for the closed SICSNs (including quantized control, sliding mode control, inner synchronization, outer synchronization, and so on) and expore the impacts on the dynamical properties of SICSNs by the coupled topology between different node systems, stochastic perturbations, impusive effects and time delays. (4) Construct some effective numerical methods for SICSNs, and carried out the simulation on the computer. (5) Try to provide a sysmatic theoretical framework for SICSNs, which will enrich the theory of complex systems, and apply our results to engineering applications, such as formation control of air or underwater vehicles.

网络化随机脉冲耦合系统(stochastic impulsive coupled systems on networks简称SICSNs)的与网络拓扑结构相关的稳定性分析和控制问题至今尚未完全解决。本项目在讨论随机（脉冲）微分方程稳定性理论和有向图理论等的基础上，研究SICSNs稳定性和能观测、能控性等控制基本理论以及多种控制综合。内容包括：利用有向图理论建立SICSNs模型；巧妙结合Lyapunov方法和有向图理论研究SICSNs的各种稳定性、分支和周期性等动力学性质，给出与SICSNs拓扑结构相关的一系列稳定性判据；研究SICSNs能观测、能控性等控制基本理论和多种控制方法、同步以及数值仿真，设计与SICSNs拓扑结构相关的控制器；把所得理论结果应用到飞行器编队和水下航行器编队控制等实际系统中。通过这项研究，有望初步形成SICSNs理论架构，并反过来促进随机脉冲微分方程理论发展和应用。

网络化随机脉冲耦合系统(stochastic impulsive coupled systems on networks简称SICSNs)的与网络拓扑结构相关的稳定性分析和控制问题至今尚未完全解决。本项目在讨论随机（脉冲）微分方程稳定性理论和有向图理论等的基础上，研究SICSNs稳定性和能观测、能控性等控制基本理论以及多种控制综合。内容包括：利用有向图理论建立SICSNs模型；巧妙结合Lyapunov方法和有向图理论研究SICSNs的各种稳定性、分支和周期性等动力学性质，给出与SICSNs拓扑结构相关的一系列稳定性判据；研究SICSNs能观测、能控性等控制基本理论和多种控制方法、同步以及数值仿真，设计与SICSNs拓扑结构相关的控制器；把所得理论结果应用到飞行器和水下航行器控制等实际系统中。通过这项研究，初步形成了SICSNs理论架构，并反过来促进了随机脉冲微分方程理论发展和应用。培养毕业研究生3人，毕业博士生5人，其中4人到国外知名大学联合培养。2020年获得山东省自然科学2等奖（首位）。培育申请到山东省基础重大项目一项。