基于能量约束的分数阶多智能体系统的一致性性能分析

The complex fractional operating environment of the multi-agent system, the communication constraints and the finite energy of agents should be considered. Based on the memory function and genetic characteristics of the fractional-order differential operator, in this project, the problems of modeling, dynamical performance analysis and the tradeoff design problem of the fractional-order multi-agent system with communication parameters are studied. These research results will provide the theoretical guidance for the application of multi-agent system in the fractional environment. The main results will include, (1) Based on the frequency domain characteristics of delay and communication noise, the fractional-order multi-agent system model with communication parameters will be established; (2) the consensus performance limitations will be discussed by employing the frequency control theory and Youla parameterization theory, and the quantitative relationship description between the consensus performance limitations and the factors such as the agent characteristics, network topology, communication parameters etc. will be presented; (3) the tradeoff optimization with the energy constraints will be studied by adopting the optimal control theory to obtain a tradeoff design criterion between the consensus performance and finite energy. The research results will broaden the content of complex systems and will also provide theoretical guidance and technical support to accelerate application of the fractional calculus theory and complex systems research in many fields such as physics, engineering and so on. This study is of important scientific significance and application value.

针对多智能体系统复杂的分数运行环境及智能体节点通讯受通信约束和有限能量约束，基于分数阶微分算子的记忆功能和遗传特性，本项目以分数阶多智能体系统为研究对象，研究融合通信参量的分数阶多智能体系统建模、动态性能及权衡设计问题，为多智能体系统在分数环境中的应用提供理论指导。主要内容包括：（1）基于时延与通信噪声的频域特性，建立反映通信参量的分数阶多智能体系统模型；（2）基于频域控制理论和Youla参数化理论研究系统的一致性性能极限，给出智能体特性、网络拓扑和通信参量等因素与一致性性能极限值的定量关系描述；（3）采用最优化控制理论分析控制能量约束的权衡优化设计问题，给出一致性性能与有限能量的权衡设计准则。其成果旨在进一步拓宽复杂系统研究内容，为加快分数阶微积分理论和复杂系统研究成果在物理、工程学等众多领域的广泛应用提供理论指导和技术支持，具有重要的科学意义和应用价值。

提出了新的反映跟踪能量、控制能量与信道能量关系的权衡性能指标，重点研究了网络通信参量影响下的权衡性能极限，建立了性能极限与网络通信参量（包括数据丢包、采样、有色噪声、有限带宽）和被控对象的本质特性之间的联系，揭示了网络通信参量给系统性能带来的不利影响。同时建立了新的修正跟踪性能指标，采用内外分解方法求得修正跟踪性能极限，并给出修正因子的适当选取范围，消除了被控对象必须含有积分器的严格假设和对参考输入信号方向的假设。基于频域分析理论，研究了一类混合分数阶多智能体系统的一致性性能，揭示了输入时延对系统一致性性能的影响。同时给出了几类分数阶混沌系统自适应同步、混合投影同步准则。给出了几类新型微分不等式，研究了几类神经网络系统的Lagrange指数稳定性、全局指数吸引集和正向不变集存在性的构造性证明，并给出了最终界和全局吸引集的精细估计式。建立新的Halanay不等式，研究了带有离散时滞和分布时滞的神经网络的全局指数稳定性、无源性和解的存在性。提出了两类激活函数可调的神经网络模型用于求解TVQP问题，分析了系统的有限时间稳定性，给出了收敛时间上界估计，并应用到机器人轨迹跟踪中。项目资助发表24篇研究论文（其中期刊论文20篇，会议论文4篇，SCI收录17篇，EI收录19篇）及7篇硕士论文。