arXivDaily arXiv每日学术速递 周一至周五更新
arXiv周末暂无论文更新,休息一下吧,周末愉快~~
arXiv 2106.00899eess.SYcs.SY
收藏

反馈互连平均场密度估计与控制

Feedback Interconnected Mean-Field Density Estimation and Control

Tongjia Zheng, Qing Han, Hai Lin

摘要:

群机器人系统在不久的将来有可预见的应用。最近,已经有越来越多的文献,采用平均场偏微分方程(PDE)来模拟群体机器人系统的概率密度的时间演化,并使用密度反馈来设计作用于个体的稳定控制律,使其密度收敛到目标轮廓。然而,它仍然在很大程度上未被探索考虑的问题,如何估计的平均场密度,密度估计算法如何影响控制性能,以及估计性能是否反过来取决于控制算法。在这项工作中,我们专注于研究这些算法的相互作用。具体来说,我们提出了新的密度控制律,使用平均场密度和梯度作为反馈,并证明了它们是全局输入到状态稳定(ISS)的估计误差。然后,我们设计了滤波算法来分别估计密度和梯度,并证明了这些估计是收敛的假设控制律是已知的。最后,我们证明了这些估计和控制算法的反馈互连仍然是全局ISS,这是由于PDE系统的双线性。一个基于代理的仿真,以验证这些算法的稳定性和他们的反馈互连。

英文摘要:

Swarm robotic systems have foreseeable applications in the near future. Recently, there has been an increasing amount of literature that employs mean-field partial differential equations (PDEs) to model the time-evolution of the probability density of swarm robotic systems and uses density feedback to design stabilizing control laws that act on individuals such that their density converges to a target profile. However, it remains largely unexplored considering problems of how to estimate the mean-field density, how the density estimation algorithms affect the control performance, and whether the estimation performance in turn depends on the control algorithms. In this work, we focus on studying the interplay of these algorithms. Specifically, we propose new density control laws which use the mean-field density and its gradient as feedback, and prove that they are globally input-to-state stable (ISS) with respect to estimation errors. Then, we design filtering algorithms to estimate the density and its gradient separately, and prove that these estimates are convergent assuming the control laws are known. Finally, we show that the feedback interconnection of these estimation and control algorithms is still globally ISS, which is attributed to the bilinearity of the PDE system. An agent-based simulation is included to verify the stability of these algorithms and their feedback interconnection.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑