Fixed-Time Flocking and Collision Avoidance Problem of a Cucker–Smale Model

Fixed-Time Flocking and Collision Avoidance Problem of a Cucker–Smale Model

Multiagent systems are used in artificial intelligence, control theory, and social sciences. In this article, we studied a Cucker–Smale model with a continuous non-Lipschitz protocol. The methodology presented in the current paper is based on the explicit construction of a Lyapunov functional. By us...

Full description

Bibliographic Details
Main Authors: Fen Nie, Xiaojun Duan
Format: Article
Language:English
Published: Hindawi Limited 2020-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2020/6080636
id doaj-198f2d04b8bb4e538d5c8850808dc802
record_format Article
spelling doaj-198f2d04b8bb4e538d5c8850808dc8022020-11-25T03:28:53ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472020-01-01202010.1155/2020/60806366080636Fixed-Time Flocking and Collision Avoidance Problem of a Cucker–Smale ModelFen Nie0Xiaojun Duan1College of Liberal Arts and Sciences, National University of Defense Technology, Changsha 410073, ChinaCollege of Liberal Arts and Sciences, National University of Defense Technology, Changsha 410073, ChinaMultiagent systems are used in artificial intelligence, control theory, and social sciences. In this article, we studied a Cucker–Smale model with a continuous non-Lipschitz protocol. The methodology presented in the current paper is based on the explicit construction of a Lyapunov functional. By using the fixed-time control technology, we show that the flocking can occur in fixed-time and collision avoiding when a singular communication function with a weighted sum of sign functions of the relative velocities among agents, and we can obtain the estimation of the converging time which is independent of the initial states of agents. Theoretical results are supported by numerical simulations.http://dx.doi.org/10.1155/2020/6080636
collection DOAJ
language English
format Article
sources DOAJ
author Fen Nie
Xiaojun Duan
spellingShingle Fen Nie
Xiaojun Duan
Fixed-Time Flocking and Collision Avoidance Problem of a Cucker–Smale Model
Mathematical Problems in Engineering
author_facet Fen Nie
Xiaojun Duan
author_sort Fen Nie
title Fixed-Time Flocking and Collision Avoidance Problem of a Cucker–Smale Model
title_short Fixed-Time Flocking and Collision Avoidance Problem of a Cucker–Smale Model
title_full Fixed-Time Flocking and Collision Avoidance Problem of a Cucker–Smale Model
title_fullStr Fixed-Time Flocking and Collision Avoidance Problem of a Cucker–Smale Model
title_full_unstemmed Fixed-Time Flocking and Collision Avoidance Problem of a Cucker–Smale Model
title_sort fixed-time flocking and collision avoidance problem of a cucker–smale model
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2020-01-01
description Multiagent systems are used in artificial intelligence, control theory, and social sciences. In this article, we studied a Cucker–Smale model with a continuous non-Lipschitz protocol. The methodology presented in the current paper is based on the explicit construction of a Lyapunov functional. By using the fixed-time control technology, we show that the flocking can occur in fixed-time and collision avoiding when a singular communication function with a weighted sum of sign functions of the relative velocities among agents, and we can obtain the estimation of the converging time which is independent of the initial states of agents. Theoretical results are supported by numerical simulations.
url http://dx.doi.org/10.1155/2020/6080636
work_keys_str_mv AT fennie fixedtimeflockingandcollisionavoidanceproblemofacuckersmalemodel
AT xiaojunduan fixedtimeflockingandcollisionavoidanceproblemofacuckersmalemodel
_version_ 1715202967032823808

Similar Items