有向拓扑结构下复杂网络系统的同步验证
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摘要:
研究了具有非线性耦合的复杂网络系统的同步验证问题.基于一般的非二次型Lyapunov函数,建立了保守性更弱的有向拓扑结构下的非线性网络系统的同步判据.对于多项式网络系统,将可同步问题转化为平方和优化问题,由此来高效地求解高阶的多项式Lyapunov函数.求解平方和优化问题隶属于凸优化框架,因此可以在多项式时间内自动地实现系统的同步验证.最后,通过一个数值仿真实例验证了理论结果的有效性,同时说明了所提出的方法可以使用一个较小的耦合强度下界来确保同步实现.
In this article,we study the problem of synchronization verification for complex networked systems with nonlinear coupling.Based on general form of Lyapunov functions,a less conservative synchronization criterion is proposed for the nonlinear networked systems with directed graph.Then,the synchronization problem for polynomial networked systems can be transformed into a sum-of-squares optimization problem,which falls within the convex optimization framework,yielding polynomial Lyapunov functions efficiently to realize the automatic synchronization verification in polynomial time.Finally,the effectiveness of the theoretical results is demonstrated by a simulation example,where the synchronization of Lorenz system is achieved by using a smaller lower bound of coupling strength.
作者:
王磊 张书源 葛思彤 刘洋
Wang Lei;Zhang Shuyuan;Ge Sitong;Liu Yang(School of Automation Science and Electrical Engineering,Beihang University,Beijing 100191,China)
机构地区:
北京航空航天大学自动化科学与电气工程学院
引用本文:
《betway官方app 学报（自然科学版）》 CAS 2024年第2期27-32,F0002,共7页
Journal of Henan Normal University(Natural Science Edition)
基金:
国家自然科学基金(61873017)。
关键词:
多项式Lyapunov函数 同步验证 复杂网络系统 平方和优化
polynomial Lyapunov functions synchronization verification complex networked systems sum-of-squares optimization
分类号:
O231.2 [理学—运筹学与控制论]
