Funnel formation control for multi-agent systems and its application to satellite formation flight

拟议的研究项目的目标是开发，数值实现和分析的新的分散控制概念漏斗形成控制（FFC）的多智能体系统。该方法能够保证智能体间距离在一定范围内演化。 此外，它实现了碰撞避免和速度同步与规定的性能，在所谓的“植绒”的上下文中。作为一个特殊的挑战，我们认为异构代理与非线性动力学。此外，代理的动态和初始状态不被假定为已知的，除了一些结构信息，如基础微分方程的阶数。为了实现这些雄心勃勃的目标，我们利用漏斗控制的方法，这是控制工程和数学系统理论的当前研究领域，它成功地平衡了理论和应用。漏斗控制器能够保证输出变量在预定裕度内的演化。这允许独立于特定系统参数的控制器设计，因此表现出固有的鲁棒性。所需的控制策略由三个部分组成：1.）在第一地层控制部分中，地层中每种药剂的期望位置被几何构造，并在最近的漏斗控制方法中用作参考信号。以这种方式构造的FFC实现了每个代理以规定的性能到达其期望的位置。此外，输入滤波器用于避免速度的测量。2.）的情况。在第二步骤中，FFC通过额外的控制器组件进行扩展，这实现了碰撞避免。该组件再次基于漏斗控制技术。对于这种组合，可行性和鲁棒性将得到严格证明。3.）第三章在最后一步中，避免碰撞的FFC与所谓的边缘漏斗耦合定律相结合，该定律实现了具有规定性能的代理的速度的同步。通过这种方式，期望实现以规定行为的智能体群集的最终目标。作为一个概念的证明，应用卫星编队飞行被认为是，其中每个卫星描述的二阶非线性微分方程。在此过程中，所开发的控制方法的性能和可实施性将通过仿真研究不断得到验证。这支持选择合适的控制器设计参数，从而确保理论和数值实践之间的连续反馈。

The objective of the proposed research project is the development, numerical implementation and analysis of the novel decentralized control concept Funnel Formation Control (FFC) for multi-agent systems. This method is able to guarantee the evolution of the inter-agent distances within a prescribed range. Additionally, it achieves collision avoidance and velocity synchronization with prescribed performance in the context of so-called “flocking”. As a particular challenge, we consider heterogeneous agents with nonlinear dynamics. Furthermore, the dynamics and initial states of the agents are not assumed to be known, apart from some structural information such as the order of the underlying differential equation. To realize these ambitious goals we utilize methods from funnel control, which is a current research area in control engineering and mathematical systems theory, and it successfully balances theory and application. The funnel controller is able to guarantee the evolution of the output variables within a prespecified margin. This allows for a controller design independent of the specific system parameters, which therefore exhibits inherent robustness properties. The desired control strategy consists of three components: 1.) In the first formation control part the desired position of each agent in the formation is constructed geometrically and used as a reference signal in a recent funnel control method. The FFC constructed in this way achieves that each agent attains its desired position with prescribed performance. Additionally, an input filter is used to avoid the measurements of velocities. 2.) In a second step the FFC is expanded by an additional controller component, which achieves collision avoidance. This component is again based on funnel control techniques. For this combination, feasibility and robustness are to be proved rigorously. 3.) In the last step the collision-avoiding FFC is combined with a so-called edge-wise funnel coupling law, which achieves synchronization of the velocities of the agents with prescribed performance. In this way it is expected to achieve the ultimate objective of flocking with prescribed behavior of the agents. As a proof of concept, the application to satellite formation flight is considered, where each satellite is described by a nonlinear differential equation of second order. In the course of this, the performance and implementability of the developed control methods is to be constantly verified by means of simulation studies. This supports the selection of suitable controller design parameters and thus ensures a continuous feedback between theory and numerical practice.