A PDE-based control concept is developed to deploy a multi-agent system into desired formation profiles. The dynamic model is based on a coupled linear, time-variant parabolic distributed parameter system. By means of a particular coupling structure parameter information can be distributed within the agent continuum. Flatness-based motion planning and feedforward control are combined with a backstepping-based boundary controller to stabilize the distributed parameter system of the tracking error. The tracking controller utilizes the required state information from a Luenberger-type state observer. By means of an exogenous system the relocation of formation profiles is achieved. The transfer of the control strategy to a finite-dimensional discrete multi-agent system is obtained by a suitable finite difference discretization of the continuum model, which in addition imposes a leader–follower communication topology. The results are evaluated both in simulation studies and in experiments for a swarm of mobile robots realizing the transition between different stable and unstable formation profiles.

开发了基于PDE的控制概念，以将多主体系统部署到所需的地层剖面中。动态模型基于耦合的线性时变抛物线分布参数系统。借助于特定的耦合结构，参数信息可以分布在代理连续体内。基于平面度的运动计划和前馈控制与基于反推的边界控制器相结合，以稳定跟踪误差的分布式参数系统。跟踪控制器利用来自Luenberger型状态观察器的所需状态信息。通过外生系统，可以实现地层剖面的重定位。通过对连续模型进行适当的有限差分离散化，可以将控制策略转移到有限维离散多主体系统中，此外，它还强加了领导者与跟随者的通信拓扑。结果在仿真研究和实验中评估了一大批可实现不同稳定和不稳定地层剖面之间过渡的移动机器人。