Ramírez Adrián, Sipahi Rifat, Mondié Sabine, Garrido Rubén
Division of Applied Mathematics, IPICYT, San Luis Potosí, SLP 78216, México.
Department of Mechanical and Industrial Engineering, Northeastern University, Boston, MA 02115, USA.
Philos Trans A Math Phys Eng Sci. 2019 Sep 9;377(2153):20180130. doi: 10.1098/rsta.2018.0130. Epub 2019 Jul 22.
This article is on fast-consensus reaching in a class of multi-agent systems (MAS). We present an analytical approach to tune controllers for the agents based on the premise that delayed measurements in the controller can be preferable to standard controllers relying only on current measurements. Controller tuning in this setting is however challenging due to the presence of delays. To tackle this problem, we propose an analytic geometry approach. The key contribution is that the tuning can be implemented for complex eigenvalues of the arising graph Laplacian of the network, complementing the current state of the art, which is limited to real eigenvalues. Results, therefore, extend our knowledge beyond symmetric graphs and enable the study of the MAS under directed graphs. This article is part of the theme issue 'Nonlinear dynamics of delay systems'.
本文研究一类多智能体系统（MAS）中的快速共识达成问题。我们提出一种分析方法，基于这样的前提来调整智能体的控制器：即控制器中的延迟测量可能比仅依赖当前测量的标准控制器更可取。然而，由于存在延迟，在这种情况下进行控制器调整具有挑战性。为解决这个问题，我们提出一种解析几何方法。关键贡献在于，对于网络中出现的图拉普拉斯矩阵的复特征值也可以进行调整，这补充了当前仅限于实特征值的技术水平。因此，研究结果扩展了我们对对称图之外的认识，并能够对有向图下的多智能体系统进行研究。本文是“延迟系统的非线性动力学”主题专刊的一部分。
