Team Control Problem in Virtual Ellipsoid and Its Numerical Simulations

Zhiqing Dang, Zhaopeng Dai, Yang Yu, Long Zhang, Ang Su, Zhihang You and Hongwei Gao
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Zhiqing Dang: School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China
Zhaopeng Dai: School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China
Yang Yu: School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China
Long Zhang: School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China
Ang Su: School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China
Zhihang You: School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China
Hongwei Gao: School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China

Mathematics, 2022, vol. 10, issue 12, 1-19

Abstract: There is tremendous interest in designing feedback strategy control for clusters in modern control theory. We propose a novel numerical solution to target team control problems by using the Hamilton formalism methods. In order to ensure the smooth wireless information exchange, all members of the team are located in a virtual ellipsoidal container during the whole movement process. An ellipsoidal container tube is constructed as the external state constraint of the team. The corresponding value function is then formulated based on collision avoidance conditions and energy constraints in the process of the team motion. Time-dependent partial differential equations are formulated based on Hamilton formalism, which have been solved numerically by using the traditional finite difference method (FDM). The objective of the presented method is to obtain optimal control and motion trajectory of the cluster at each moment. Lastly, we conduct a simulation study of unmanned aerial vehicles (UAVs) to demonstrate the performance of the proposed method.

Keywords: ellipsoidal trajectory; team control; value function; finite difference method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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