<p>This work investigates prescribed-time flocking control with collision avoidance for Cucker-Smale systems. The authors propose a novel control framework that guarantees prescribed-time flocking, with convergence time that are both independent of initial conditions and control parameters. Within the framework of Lyapunov stability theory, the authors derive sufficient conditions guaranteeing both flocking convergence and collision avoidance in Cucker-Smale systems. In addition, an upper bound for the energy required to achieve flocking is theoretically derived. The results indicate that parameters <i>α</i> and <i>β</i> significantly affect the system’s flocking dynamics. Specifically, parameter <i>α</i> exhibits a nonmonotonic relationship with convergence speed and energy cost, revealing a fundamental performance trade-off. In contrast, reducing parameter <i>β</i> simultaneously improves convergence speed and decreases energy cost. Furthermore, the prescribed time <i>T</i><sub><i>p</i></sub> and system size <i>N</i> are critical factors that substantially affect energy consumption. The results provide theoretical foundations for designing efficient flocking controllers and balancing the trade-off between convergence speed and energy cost.</p>

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Prescribed-Time Flocking Control of Cucker-Smale Systems with Collision Avoidance

  • Rui Xiao,
  • Huimin Wang,
  • Meixin Zhen,
  • Xiangxin Yin

摘要

This work investigates prescribed-time flocking control with collision avoidance for Cucker-Smale systems. The authors propose a novel control framework that guarantees prescribed-time flocking, with convergence time that are both independent of initial conditions and control parameters. Within the framework of Lyapunov stability theory, the authors derive sufficient conditions guaranteeing both flocking convergence and collision avoidance in Cucker-Smale systems. In addition, an upper bound for the energy required to achieve flocking is theoretically derived. The results indicate that parameters α and β significantly affect the system’s flocking dynamics. Specifically, parameter α exhibits a nonmonotonic relationship with convergence speed and energy cost, revealing a fundamental performance trade-off. In contrast, reducing parameter β simultaneously improves convergence speed and decreases energy cost. Furthermore, the prescribed time Tp and system size N are critical factors that substantially affect energy consumption. The results provide theoretical foundations for designing efficient flocking controllers and balancing the trade-off between convergence speed and energy cost.