具无穷维复频算子多智能体的函数空间蜂拥与控制

Control theory and applications for trajectory flocking in function spaces of multi-agents with infinite-dimensional complex/frequency-domain operators (ICO) are suggested. ICO multi-agent networks include networked configurations with multiple agents, which possess modeling expressions about dynamics, statics, and parameters in terms of ICO’s. Such networks exist when the multi-agents are periodically time-varying, sampled-data controlled, time-delayed, distributed in states, input/output and parameters. In the literature, multi-agent flocking is usually viewed pointwisely in Euclidean space x time and in the asymptotic convergence sense. Consequently, asymptotic convergence analysis is frequently exploited for flocking and its control algorithms. This approach is inconvenient in accommodating ICO multi-agents during performance evaluation and control algorithm design whenever flocking trajectories other than those around t→∞ are involved. ..In the project, ICO multi-agent flocking is dealt with in trajectory viewpoint, rather than pointwisely with respect to positions. We will re-formulate the multi-agent flocking in Euclidean spaces under pointwise position vector norms, or pointwise flocking, into ones in function spaces under trajectory function norms, or trajectory flocking．The variation follows if the multi-agents in Euclidean spaces can be re-modeled by infinite-dimensional complex/frequency-domain operators on function spaces such that multi-agent flocking in Euclidean space x time has a multi-operator counterpart in function spaces. Since function spaces have exquisite structures and functional characteristics, trajectory flocking opens an alternative horizon that may reorganize and consolidate multi-agent problem formulations and their solutions such as consensus, synchronization, formation, tracking, virtual leadership and etc. ..ICO multi-agent flocking and its control will be considered with complex/frequency-domain multi-operators in probably infinite-dimensional Banach or Hilbert function spaces. By operator algebras, trajectory flocking will be introduced and examined. More specifically, existence conditions and control algorithms for trajectory flocking in ICO multi-agents will be worked out by expanding the complex/frequency-domain analysis and synthesis theory and techniques for linear time-invariant systems. Studying trajectory flocking will deepen and enrich our interpretation about flocking phenomena, together with asymptotic convergence behavior, and facilitate their control applications. ..ICO plants confront us in multi-machine power systems, where the prototype idea emerges, and common control strategies involve complicated actuators due to communication delays, high maintenance cost. The project will benefit the power industry beside others, with theoretical results and methodological derivatives.

对个体动态/静态/参量等具有无穷维复频域算子描述的多智能体网络，建立复频域算子群模型，讨论其在函数空间实现多智能体群体目标的运动轨迹意义的蜂拥及其控制。项目对具周期时变，采样值，时滞，分布参数，部分非线性等的多智能体蜂拥控制的分析与设计有意义。具体地，将多智能体的欧氏空间乘时间域的点态向量范数意义的蜂拥，或点态蜂拥，转换为函数空间的轨迹向量函数范数意义的蜂拥，或轨迹蜂拥；在定义函数空间Reynolds蜂拥规则后，讨论存在特性并探索基于无穷维复频域理论的控制算法构成与参数化。函数空间具结构完备性和泛函解析多样性，将欧氏空间点态蜂拥扩展为函数空间轨迹蜂拥有理论必然和技术可能。函数空间轨迹蜂拥及其控制算法的解明将为协同，同步，编队，跟踪，虚拟领导等多智能体控制问题提供具精确性和一致性的理论基础与技术整合平台。学术挑战性毋庸置疑，对多机电力网络类多智能体控制技术研发有工程价值和技术创新前景。

该结题项目以探讨多智能体个体的动态/静态/参量等具有无穷维复频域算子模型（如时滞，周期时变，采样值等）的多智能体网络系统的蜂拥控制分析与设计问题；主要研究内容是，通过构建智能体个体和整体的复频域算子模型并利用复频域分析方法，讨论对其实施定义于函数空间的蜂拥控制时，多智能体网络系统所具有的主要性质与工程应用可能性。..在研究过程中，已经取得的关于多智能体的重要结果包括：.1）二阶自驱动粒子型多智能体网络的平均值（位置，速度）轨迹计算公式的成功推导，解明了这类系统的可控制，可观性等结构特性，由此使得扩展Olftai-Saber蜂拥控制算法结构和参数整定原则从定性与定量两方面都得到透彻的解释；这一部分的理论成果为我们将成熟的极点配置，最小均方调节优化，滑模控制，鲁棒控制等方法扩展到多智能体网络控制上，提供了坚实的理论基础；.2）二阶自驱动粒子型多智能体群的基于密集分布的初始状态的碰撞和基于权重系数度量调整的碰撞诱发机理得到严格的证实；这一部分的理论结果，既为为多智能体群体运动中的避碰/避障控制设计提供了理论依据，也为多智能体群的广义一致性控制问题给出了新的解决方案；.3）对具有无穷维复频域算子个体化复杂系统，如时滞的，周期时变的，采样值的和Lure非线性等系统，引入了复频域尺度缩放的概念与方法，使得这些类型的个体化系统的稳定分析与镇定设计问题得以极大地摆脱对开环系统特性的依赖，简化了复频域分析的限制条件和设计步骤，为具有无穷维复频域算子模型的多智能体协同控制的复频域分析与设计奠定了理论基础。..结题项目的上述重要理论成果，一方面，集中在在函数空间概念上和复频域分析设计方法上，极大地完善和丰富了我们对蜂拥控制的复函分析方法的理解与认识；另一方面，为多智能体控制理论在多机电力系统协同控制工程技术的创新发展提供了新的技术可能性，有十分明确的工程技术指导价值。