Flocking analysis and control of a nonlinear collective migration model

Abstract In this paper, we study a nonlinear collective migration model with the Cucker–Smale type weight, the nonlinear velocity coupling and the distributed network. Finite-time flocking tracking can be achieved by the alignment force gathering agents and the tracking force matching target. A trade-off existing between the two forces is established by the tracking strategy that can be viewed as a control. When the strategy is time-invariant, finite-time flocking tracking would occur for any initial state under the long-range weight, only for partial initial state under the short-range weight. An invariant set of the system is proposed and proved to be an attractive domain of the flocking state. Then two time-varying strategies, the average strategy and the maximum strategy, are designed to overcome the constraint of initial state under the short-range weight. The average strategy has to mobilize all agents simultaneously, but only causes once switch. The maximum strategy only mobilizes the agent with the largest velocity deviation, but produces more switches. Several numerical simulations are provided to observe the effects of the time-invariant and time-varying strategies.