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分数阶时滞广义Logistic方程解的研究 被引量:3
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作者 袁利国 《中山大学学报(自然科学版)》 CAS CSCD 北大核心 2014年第2期44-48,共5页
基于Banach不动点定理与分数阶微积分的相关性质,首先研究了分数阶时滞广义Logistic方程解的存在唯一性,同时得到解的一致稳定性的充分条件。最后,利用改进的Adams-Bashforth-Moulton预估-校正算法得到其数值解。
关键词 CAPUTO分数阶导数 分数阶时滞Logistic方程 banach不动点定理 存在唯一性
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Banach不动点定理在非线性发展变分不等式解的讨论中的应用 被引量:1
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作者 高斐 王希营 丁方允 《兰州大学学报(自然科学版)》 CAS CSCD 北大核心 2003年第2期9-11,共3页
利用 Banach不动点定理给出了一类由粘弹接触问题引出的非线性发展变分不等式解的存在惟一性 。
关键词 banach不动点定理 粘弹接触问题 非线性发展变分不等式 LIPsCHITZ连续 强单调性
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A modified consensus algorithm for multi-UAV formations based on pigeon-inspired optimization with a slow diving strategy
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作者 ZHANG Tianjie DUAN Haibin 《智能系统学报》 CSCD 北大核心 2017年第4期570-581,共12页
This paper considers the formation control problem for a group of unmanned aerial vehicles( UAVs)employing consensus with different optimizers. A group of UAVs can never accomplish difficult tasks without formation be... This paper considers the formation control problem for a group of unmanned aerial vehicles( UAVs)employing consensus with different optimizers. A group of UAVs can never accomplish difficult tasks without formation because if disordered they do not work any better than a single vehicle,and a single vehicle is limited by its undeveloped intelligence and insufficient load. Among the many formation methods,consensus has attracted much attention because of its effectiveness and simplicity. However,at the beginning of convergence,overshoot and oscillation are universal because of the limitation of communication and a lack of forecasting,which are inborn shortcomings of consensus. It is natural to modify this method with lots of optimizers. In order to reduce overshoot and smooth trajectories, this paper first adopted particle swarm optimization( PSO), then pigeon-inspired optimization( PIO) to modify the consensus. PSO is a very popular optimizer,while PIO is a new method,both work but still retain disadvantages such as residual oscillation. As a result,it was necessary to modify PIO,and a pigeon-inspired optimization with a slow diving strategy( SD-PIO) is proposed. Convergence analysis was performed on the SD-PIO based on the Banach fixed-point theorem and conditions sufficient for stability were achieved.Finally,a series of comparative simulations were conducted to verify the feasibility and effectiveness of the proposed approach. 展开更多
关键词 unmanned aerial vehicle(UAV) formation consensus pigeon-inspired optimization(PIO) banach fixed-point theorem
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