具有马尔科夫跳变的随机复杂网络有限时间同步控制

The research on synchronization control of stochastic complex networks is a hot research topic involving multidisciplinary interdisciplinary such as control, mathematics and communication and so on. The finite-time synchronization describes the transient performance of the system and has a wide application value. This project intends to investigate the finite-time synchronization control problem for the stochastic complex network with Markov jumps on the basis of previous related research accumulations. First of all, taking full account of various constraint communication factors, the mathematical model that meets the actual conditions of engineering is established. And by taking advantages of various control methods such as impulsive control, pinning control, intermittent control, adaptive control and other control methods, the simple and easy-to-implement finite-time synchronization control protocol is designed. Secondly, using the incomplete information of complex transition probabilities, the low-conservation and easy-to-verify finite-time synchronization criteria are obtained by means of Lyapunov functions/functional methods, inequality techniques, and other analytical techniques. Finally, the dynamic behavior of semi-Markov jump system is deeply analyzed and a solution to the finite-time synchronization control of stochastic complex network with semi-Markov jump is given. Based on the synchronization analysis, the coupling relationship between the constrained factors, switching modes, control parameters and system performance is further explored. The research of this project will enrich the theory of stochastic complex networks and provide theoretical basis for its engineering practice application.

随机复杂网络同步控制研究是控制、数学、通信等多学科交叉性热门研究课题。有限时间同步描述了系统的暂态性能，具有广泛的应用。基于前期相关的研究积累，本项目拟针对具有马尔科夫跳变的随机复杂网络，深入研究其有限时间同步控制问题。首先，充分考虑各种通信受限因素，建立符合工程实际的数学模型，并综合利用脉冲控制、牵制控制、间歇控制、自适应控制等多种控制方法各自的优势，设计简单易行的有限时间同步控制协议；其次，利用复杂转移概率的不完全信息，借助Lyapunov函数/泛函法、不等式技巧等多种分析技巧和方法，获得保守性低且易于验证的有限时间同步判据；最后，深入剖析半马尔科夫跳变系统的动力学行为，给出半马尔科夫跳变随机复杂网络有限时间同步控制的解决方案，并在同步分析的基础上，进一步探究受限因素、跳变模态、控制参数与系统性能之间的耦合关系。本项目研究成果将进一步丰富随机复杂网络理论，为其工程实践应用提供理论依据。

复杂网络的同步控制问题是多个领域的研究热点问题。对于随机复杂网络有限时间同步问题的研究不仅具有重要的学术价值而且有实际应用意义。研究工作按照项目计划完成，圆满完成了预期研究目标。本项目成果主要包括：（1）针对具有通信受限（时滞、丢包）的马尔科夫跳变随机复杂网络，设计了自适应控制器、脉冲牵制控制器，研究了有限时间、固定时间同步问题；（2）针对具有复杂转移概率的马尔科夫跳变系统研究了有限时间同步控制问题；（3）并进一步推广到半马尔科夫跳变情形。在既定的研究内容基础上，进行了一系列的扩展研究：（4）时变线性随机马尔可夫跳跃系统的几乎必然稳定性、指数稳定性；（5）基于复杂多智能体网络的优化问题；（6）针对信息物理系统的入侵检测与识别；（7）智能系统行为设计、服务设计等。目前为止共发表学术论文30篇，其中SCI收录16篇，申请发明专利1项，授权1项。本项目系列研究成果进一步丰富了复杂网络同步控制的理论。