具有领导者驱动的多智能体系统三维空间编队的延迟自适应补偿器
Delay-Adaptive Compensator for 3-D Space Formation of Multi-Agent Systems with Leaders Actuation
AI总结：
本文针对三维空间中受未知延迟影响的领导者驱动的多智能体系统，提出基于PDE反推和Lyapunov泛函的延迟自适应控制器，实现编队状态调节。
摘要：
本文关注在大规模多智能体系统（MAS）在三维空间中运行的集体动力学控制，特别强调补偿影响被驱动领导者的未知延迟的影响。智能体的通信图定义在网格状的二维圆柱面上。我们通过复值和实值的反应-对流-扩散二维偏微分方程（PDE）对智能体的集体动力学进行建模，其状态代表智能体的三维位置坐标。边界上的领导者智能体由于累积的计算和信息传输时间而遭受未知的执行器延迟。我们通过使用PDE反推结合Lyapunov泛函方法为二维PDE设计了一个延迟自适应控制器，其中后者用于设计更新律，以生成未知延迟的实时估计。利用我们最近关于具有未知输入延迟的一维抛物型PDE控制的结果，我们使用傅里叶级数展开将一维PDE的控制桥接到二维PDE的控制。为了设计二维系统的更新律，定义了一个新的目标系统，以在假设对空间分布植物状态进行测量的情况下，建立系统轨迹在$H^2$范数中的闭环局部有界性以及状态调节到零。我们通过数值模拟展示了延迟自适应控制器的性能。
英文摘要：
This paper focuses on the control of collective dynamics in large-scale multi-agent systems (MAS) operating in a 3-D space, with a specific emphasis on compensating for the influence of an unknown delay affecting the actuated leaders. The communication graph of the agents is defined on a mesh-grid 2-D cylindrical surface. We model the agents' collective dynamics by a complex- and a real-valued reaction-advection-diffusion 2-D partial differential equations (PDEs) whose states represent the 3-D position coordinates of the agents. The leader agents on the boundary suffer unknown actuator delay due to the cumulative computation and information transmission time. We design a delay-adaptive controller for the 2-D PDE by using PDE backstepping combined with a Lyapunov functional method, where the latter is employed to design an update law that generates real-time estimates of the unknown delay. Capitalizing on our recent result on the control of 1-D parabolic PDEs with unknown input delay, we use Fourier series expansion to bridge the control of 1-D PDEs to that of 2-D PDEs. To design the update law for the 2-D system, a new target system is defined to establish the closed-loop local boundedness of the system trajectories in $H^2$ norm and the regulation of the states to zero assuming a measurement of the spatially distributed plant's state. We illustrate the performance of delay-adaptive controller by numerical simulations.
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