On Collision Avoiding Fixed-Time Flocking with Measurable Diameter to a Cucker-Smale-Type Self-Propelled Particle Model

Dealing with the fixed-time flocking issue is one of the most challenging problems for a Cucker–Smale-type self-propelled particle model. In this article, the fixed-time flocking is established by employing a fixed-time stability theorem when the communication weight function has a positive infimum. Compared with the initial condition-based finite-time stability, an upper bound of the settling time in this paper is merely dependent on the design parameters. Moreover, the size of the final flocking can be estimated by the number of particles and the initial states of the system. In addition, a sufficient condition is formulated to guarantee that all particles do not collide during the process of the flocking. These results can give a reasonable explanation to some flocking phenomena such as bird flocks, fish schools, or human group behaviors. Finally, three numerical examples are granted to display the performance of the obtained results.

[1]  Alessandro Astolfi,et al.  Homogeneous Approximation, Recursive Observer Design, and Output Feedback , 2008, SIAM J. Control. Optim..

[2]  Jesús Rosado,et al.  Asymptotic Flocking Dynamics for the Kinetic Cucker-Smale Model , 2010, SIAM J. Math. Anal..

[3]  Axel Klar,et al.  SELF-PROPELLED INTERACTING PARTICLE SYSTEMS WITH ROOSTING FORCE , 2010 .

[4]  Yicheng Liu,et al.  FLOCKING AND PATTERN MOTION IN A MODIFIED CUCKER-SMALE MODEL , 2016 .

[5]  Zhihong Man,et al.  Finite-time and fixed-time leader-following consensus for multi-agent systems with discontinuous inherent dynamics , 2018, Int. J. Control.

[6]  Abdelkader Abdessameud,et al.  Formation control of VTOL Unmanned Aerial Vehicles with communication delays , 2011, Autom..

[7]  Yicheng Liu,et al.  On non-collision flocking and line-shaped spatial configuration for a modified singular Cucker-Smale model , 2019, Commun. Nonlinear Sci. Numer. Simul..

[8]  Tao Li,et al.  Finite-Time Consensus for Leader-Following Second-Order Multi-Agent Networks , 2012, IEEE Transactions on Circuits and Systems I: Regular Papers.

[9]  Jinde Cao,et al.  Nonsmooth Finite-Time Synchronization of Switched Coupled Neural Networks , 2016, IEEE Transactions on Cybernetics.

[10]  Wei Ren,et al.  Distributed Cooperative Attitude Synchronization and Tracking for Multiple Rigid Bodies , 2010, IEEE Transactions on Control Systems Technology.

[11]  Jorge Cortés,et al.  Finite-time convergent gradient flows with applications to network consensus , 2006, Autom..

[12]  Yingmin Jia,et al.  Finite-time consensus for second-order stochastic multi-agent systems with nonlinear dynamics , 2015, Appl. Math. Comput..

[13]  Jinzhi Wang,et al.  Fixed-time coordinated tracking for second-order multi-agent systems with bounded input uncertainties , 2016, Syst. Control. Lett..

[14]  Jinde Cao,et al.  Finite-time synchronisation control of complex networks via non-smooth analysis , 2015 .

[15]  Wei Zhang,et al.  Finite-time synchronization of uncertain unified chaotic systems based on CLF☆ , 2009 .

[16]  Guanghui Wen,et al.  Distributed finite-time tracking control for nonlinear multi-agent systems subject to external disturbances , 2013, Int. J. Control.

[17]  Yicheng Liu,et al.  Flocking and asymptotic velocity of the Cucker–Smale model with processing delay , 2014 .

[18]  Xiaoyang Liu,et al.  Further results on finite‐time consensus of second‐order multi‐agent systems without velocity measurements , 2016 .

[19]  Mahdi Pourgholi,et al.  Fixed-time leader–follower consensus tracking of second-order multi-agent systems with bounded input uncertainties using non-singular terminal sliding mode technique , 2017 .

[20]  Felipe Cucker,et al.  A General Collision-Avoiding Flocking Framework , 2011, IEEE Transactions on Automatic Control.

[21]  Cristina Pignotti,et al.  Flocking estimates for the Cucker–Smale model with time lag and hierarchical leadership , 2017, Journal of Mathematical Analysis and Applications.

[22]  V. Haimo.  Finite time controllers , 1986 .

[23]  Seung-Yeal Ha,et al.  On collision-avoiding initial configurations to Cucker-Smale type flocking models , 2012 .

[24]  Yuchen Han,et al.  Finite-time flocking problem of a Cucker-smale-type self-propelled particle model , 2016, Complex..

[25]  Mingjie Cai,et al.  Adaptive neural finite-time control for a class of switched nonlinear systems , 2015, Neurocomputing.

[26]  Zongyu Zuo,et al.  Nonsingular fixed-time consensus tracking for second-order multi-agent networks , 2015, Autom..

[27]  Zhuchun Li,et al.  Emergent behavior of Cucker-Smale flocking particles with heterogeneous time delays , 2018, Appl. Math. Lett..

[28]  Haijun Jiang,et al.  Finite-time and fixed-time synchronization of discontinuous complex networks: A unified control framework design , 2018, J. Frankl. Inst..

[29]  Yongcan Cao,et al.  Finite-time consensus for multi-agent networks with unknown inherent nonlinear dynamics , 2013, Autom..

[30]  Michael Defoort,et al.  Leader-follower fixed-time consensus for multi-agent systems with unknown non-linear inherent dynamics , 2015 .

[31]  Dennis S. Bernstein,et al.  Finite-Time Stability of Continuous Autonomous Systems , 2000, SIAM J. Control. Optim..

[32]  Seung-Yeal Ha,et al.  Emergence of time-asymptotic flocking in a stochastic Cucker-Smale system , 2009 .

[33]  Zongyu Zuo,et al.  Distributed robust finite-time nonlinear consensus protocols for multi-agent systems , 2016, Int. J. Syst. Sci..

[34]  Guanghui Wen,et al.  Neuro-Adaptive Consensus Tracking of Multiagent Systems With a High-Dimensional Leader , 2017, IEEE Transactions on Cybernetics.

[35]  Lin Wang,et al.  Impacts of time delay on flocking dynamics of a two-agent flock model , 2019, Commun. Nonlinear Sci. Numer. Simul..

[36]  Andrey Polyakov,et al.  Nonlinear Feedback Design for Fixed-Time Stabilization of Linear Control Systems , 2012, IEEE Transactions on Automatic Control.

[37]  Jianhong Shen,et al.  Cucker–Smale Flocking under Hierarchical Leadership , 2006, q-bio/0610048.

[38]  Tingwen Huang,et al.  Fixed-time stability of dynamical systems and fixed-time synchronization of coupled discontinuous neural networks , 2017, Neural Networks.

[39]  James Lam,et al.  Finite-Time Consensus of Multiagent Systems With a Switching Protocol , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[40]  Hongliang Liu,et al.  A note on the fixed-time bipartite flocking for nonlinear multi-agent systems , 2020, Appl. Math. Lett..

[41]  Felipe Cucker,et al.  Emergent Behavior in Flocks , 2007, IEEE Transactions on Automatic Control.

[42]  Xiangyu Wang,et al.  Finite-time consensus and collision avoidance control algorithms for multiple AUVs , 2013, Autom..