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一种分形插值曲线上的调和结构和有效电阻
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作者 冯志刚 张蓓蓓 《江苏大学学报(自然科学版)》 EI CAS 北大核心 2011年第2期245-248,共4页
为了研究分形插值曲线上的调和分析问题,根据分形曲线的生成特点,从其自相似结构出发,在一种自仿射分形插值曲线上,通过边界点集上自相似拉普拉斯变换的构造,建立了插值曲线上的电阻网络,运用有限网络中拉普拉斯变换限制的方法,给出了... 为了研究分形插值曲线上的调和分析问题,根据分形曲线的生成特点,从其自相似结构出发,在一种自仿射分形插值曲线上,通过边界点集上自相似拉普拉斯变换的构造,建立了插值曲线上的电阻网络,运用有限网络中拉普拉斯变换限制的方法,给出了相应的调和结构.结果表明该分形集的调和结构是由满足一定条件的比例系数与二阶对称矩阵构成的.同时从电学角度定义了顶点集中任意两点间与拉普拉斯变换相关的有效电阻,这样定义的有效电阻是顶点集上的一个度量,从而得到了此类插值曲线上一个新的度量空间. 展开更多
关键词 调和结构 有效电阻 电阻网络 自仿射分形插值曲线 迭代
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Leader-following coordination of multiple UUVs formation under two independent topologies and time-varying delays 被引量:5
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作者 严浙平 刘一博 +1 位作者 于长斌 周佳加 《Journal of Central South University》 SCIE EI CAS CSCD 2017年第2期382-393,共12页
The new method which uses the consensus algorithm to solve the coordinate control problems of multiple unmanned underwater vehicles (multi-UUVs) formation in the case of leader-following is adapted. As the communica... The new method which uses the consensus algorithm to solve the coordinate control problems of multiple unmanned underwater vehicles (multi-UUVs) formation in the case of leader-following is adapted. As the communication between the UUVs is difficult and it is easy to be interfered under the water, time delay is assumed to be time-varying during the members communicate with each other. Meanwhile, the state feedback linearization method is used to transfer the nonlinear and coupling model of UUV into double-integrator dynamic. With this simplified double-integrator math model, the UUV formation coordinate control is regarded as consensus problem with time-varying communication delays. In addition, the position and velocity topologies are adapted to reduce the data volume in each data packet which is sent between members in formation. With two independent topologies designed, two cases of communication delay which are same and different are considered and the sufficient conditions are proposed and analyzed. The stability of the multi-UUVs formation is proven by using Lyapunov-Razumilkhin theorem. Finally, the simulation results are presented to confirm and illustrate the theoretical results. 展开更多
关键词 multiple unmanned underwater vehicles formation consensus algorithm Lyapunov-Razumikhin theory time-varying delay state feedback linearization method
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