Cucker-Smale系统中每个个体与其相邻个体的联系对其他个体产生有限的局部影响,最终实现全部个体状态一致。该系统被广泛应用于生态网络、控制理论、通信工程、模式识别和仿生学等领域。本文根据Cucker-Smale系统的控制研究现状,介绍了...Cucker-Smale系统中每个个体与其相邻个体的联系对其他个体产生有限的局部影响,最终实现全部个体状态一致。该系统被广泛应用于生态网络、控制理论、通信工程、模式识别和仿生学等领域。本文根据Cucker-Smale系统的控制研究现状,介绍了近期取得的理论成果,包括Cucker-Smale系统渐进和牵引蜂拥、带有噪声和时滞影响下的Cucker-Smale系统蜂拥、具有leader-follow关系的Cucker-Smale系统蜂拥。进一步详细介绍了牵引蜂拥及具有leader-follow关系的Cucker-Smale系统蜂拥控制的优点,同时给出下一步需要解决的具体问题。In the Cucker-Smale system, the interaction between each individual and its neighboring individuals exerts a limited local influence on other individuals, ultimately leading to consensus among all individuals. This system has been widely applied in various fields such as ecological networks, control theory, communication engineering, pattern recognition, and bionics. In this article, based on the current status of control research on the Cucker-Smale system, we introduce recent theoretical achievements, including asymptotic and pinning swarming of the Cucker-Smale system, swarming of the Cucker-Smale system with noise and time delay effects, and swarming of the Cucker-Smale system with leader-follow relationships. Further detailed introduction was given to the advantages of pinning swarming and the crowding control of the Cucker-Smale system with the leader-follow relationship while providing specific issues to be addressed in the next step.展开更多
In this paper, we study the flocking behavior of a thermodynamic Cucker–Smale model with local velocity interactions. Using the spectral gap of a connected stochastic matrix, together with an elaborate estimate on pe...In this paper, we study the flocking behavior of a thermodynamic Cucker–Smale model with local velocity interactions. Using the spectral gap of a connected stochastic matrix, together with an elaborate estimate on perturbations of a linearized system, we provide a sufficient framework in terms of initial data and model parameters to guarantee flocking. Moreover, it is shown that the system achieves a consensus at an exponential rate.展开更多
We study the global existence and uniqueness of a strong solution to the kinetic thermomechanical Cucker-Smale(for short,TCS) model coupled with Stokes equations in the whole space.The coupled system consists of the k...We study the global existence and uniqueness of a strong solution to the kinetic thermomechanical Cucker-Smale(for short,TCS) model coupled with Stokes equations in the whole space.The coupled system consists of the kinetic TCS equation for a particle ensemble and the Stokes equations for a fluid via a drag force.In this paper,we present a complete analysis of the existence of global-in-time strong solutions to the coupled model without any smallness restrictions on the initial data.展开更多
In this paper,the flocking behavior of a Cucker-Smale model with a leader and noise is studied in a finite time.The authors present a Cucker-Smale system with two nonlinear controls for a complex network with stochast...In this paper,the flocking behavior of a Cucker-Smale model with a leader and noise is studied in a finite time.The authors present a Cucker-Smale system with two nonlinear controls for a complex network with stochastic synchronization in probability.Based on the finite-time stability theory of stochastic differential equations,the sufficient conditions for the flocking of stochastic systems in a finite time are obtained by using the Lyapunov function method.Finally,the numerical simulation of the particle system is carried out for the leader and noise,and the correctness of the results is verified.展开更多
This paper analyzes the multi-cluster flocking behavior of a Cucker-Smale model involving delays and a short-range communication weight.In each sub-flocking group,the velocity between agents is alignment and the posit...This paper analyzes the multi-cluster flocking behavior of a Cucker-Smale model involving delays and a short-range communication weight.In each sub-flocking group,the velocity between agents is alignment and the position locates at a limited domain;but in different sub-flocking groups,the position between agents is unbounded.By constructing dissipative differential inequalities of subensembles together with Lyapunov functional methods,the authors provide the sufficient condition for the multi-cluster flocking emerging.The sufficient condition includes the estimation of the range of coupling strength and the upper bound of time delay.As a result,the authors show that the coupling strength among agents and initial threshold value determine the multi-cluster flocking behavior of the delayed Cucker-Smale model.展开更多
We study the large-time dynamics of Cucker-Smale(C-S)flocking particles interacting with nonNewtonian incompressible fluids.Dynamics of particles and fluids were modeled using the kinetic Cucker-Smale equation for par...We study the large-time dynamics of Cucker-Smale(C-S)flocking particles interacting with nonNewtonian incompressible fluids.Dynamics of particles and fluids were modeled using the kinetic Cucker-Smale equation for particles and non-Newtonian Navier-Stokes system for fluids,respectively and these two systems are coupled via the drag force,which is the main flocking(alignment)mechanism between particles and fluids.We present a global existence theory for weak solutions to the coupled Cucker-Smale-Navier-Stokes system with shear thickening.We also use a Lyapunov functional approach to show that sufficiently regular solutions approach flocking states exponentially fast in time.展开更多
文摘Cucker-Smale系统中每个个体与其相邻个体的联系对其他个体产生有限的局部影响,最终实现全部个体状态一致。该系统被广泛应用于生态网络、控制理论、通信工程、模式识别和仿生学等领域。本文根据Cucker-Smale系统的控制研究现状,介绍了近期取得的理论成果,包括Cucker-Smale系统渐进和牵引蜂拥、带有噪声和时滞影响下的Cucker-Smale系统蜂拥、具有leader-follow关系的Cucker-Smale系统蜂拥。进一步详细介绍了牵引蜂拥及具有leader-follow关系的Cucker-Smale系统蜂拥控制的优点,同时给出下一步需要解决的具体问题。In the Cucker-Smale system, the interaction between each individual and its neighboring individuals exerts a limited local influence on other individuals, ultimately leading to consensus among all individuals. This system has been widely applied in various fields such as ecological networks, control theory, communication engineering, pattern recognition, and bionics. In this article, based on the current status of control research on the Cucker-Smale system, we introduce recent theoretical achievements, including asymptotic and pinning swarming of the Cucker-Smale system, swarming of the Cucker-Smale system with noise and time delay effects, and swarming of the Cucker-Smale system with leader-follow relationships. Further detailed introduction was given to the advantages of pinning swarming and the crowding control of the Cucker-Smale system with the leader-follow relationship while providing specific issues to be addressed in the next step.
文摘In this paper, we study the flocking behavior of a thermodynamic Cucker–Smale model with local velocity interactions. Using the spectral gap of a connected stochastic matrix, together with an elaborate estimate on perturbations of a linearized system, we provide a sufficient framework in terms of initial data and model parameters to guarantee flocking. Moreover, it is shown that the system achieves a consensus at an exponential rate.
基金supported by the National Natural Science Foundation of China (12001033)。
文摘We study the global existence and uniqueness of a strong solution to the kinetic thermomechanical Cucker-Smale(for short,TCS) model coupled with Stokes equations in the whole space.The coupled system consists of the kinetic TCS equation for a particle ensemble and the Stokes equations for a fluid via a drag force.In this paper,we present a complete analysis of the existence of global-in-time strong solutions to the coupled model without any smallness restrictions on the initial data.
基金supported by the Natural Science Foundation of Heilongjiang Province of China under Grant No.LH2023A007the National Natural Science Foundation of China under Grant No.11201095+2 种基金the Fundamental Research Funds for the Central Universities under Grant Nos.3072022TS2402 and 3072024GH2402the Postdoctoral Research Startup Foundation of Heilongjiang under Grant No.LBH-Q14044the Science Research Funds for Overseas Returned Chinese Scholars of Heilongjiang Province under Grant No.LC201502.
文摘In this paper,the flocking behavior of a Cucker-Smale model with a leader and noise is studied in a finite time.The authors present a Cucker-Smale system with two nonlinear controls for a complex network with stochastic synchronization in probability.Based on the finite-time stability theory of stochastic differential equations,the sufficient conditions for the flocking of stochastic systems in a finite time are obtained by using the Lyapunov function method.Finally,the numerical simulation of the particle system is carried out for the leader and noise,and the correctness of the results is verified.
基金supported by the National Natural Science Foundation of China under Grant Nos.11671011and 11428101。
文摘This paper analyzes the multi-cluster flocking behavior of a Cucker-Smale model involving delays and a short-range communication weight.In each sub-flocking group,the velocity between agents is alignment and the position locates at a limited domain;but in different sub-flocking groups,the position between agents is unbounded.By constructing dissipative differential inequalities of subensembles together with Lyapunov functional methods,the authors provide the sufficient condition for the multi-cluster flocking emerging.The sufficient condition includes the estimation of the range of coupling strength and the upper bound of time delay.As a result,the authors show that the coupling strength among agents and initial threshold value determine the multi-cluster flocking behavior of the delayed Cucker-Smale model.
基金supported by the Samsung Science and Technology Foundation (Grant No. SSTF-BA1401-03)Hwa Kil Kim was supported by the National Research Foundation of Korea (Grant No. NRF2015R1D1A1A01056696)+1 种基金Jae-Myoung Kim was supported by BK21 PLUS SNU Mathematical Sciences Divisionthe National Research Foundation of Korea (Grant No. NRF-2016R1D1A1B03930422)
文摘We study the large-time dynamics of Cucker-Smale(C-S)flocking particles interacting with nonNewtonian incompressible fluids.Dynamics of particles and fluids were modeled using the kinetic Cucker-Smale equation for particles and non-Newtonian Navier-Stokes system for fluids,respectively and these two systems are coupled via the drag force,which is the main flocking(alignment)mechanism between particles and fluids.We present a global existence theory for weak solutions to the coupled Cucker-Smale-Navier-Stokes system with shear thickening.We also use a Lyapunov functional approach to show that sufficiently regular solutions approach flocking states exponentially fast in time.
