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
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, 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
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.
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.
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.
