Abstract
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.
Highlights
In the last few years, the cooperative control of self-propelled agent systems has attracted considerable attention, mainly due to its broad range of potential applications including formation control [1], attitude alignment [2], and target tracking [3]
In our real life, phenomena in which particles reach to flock in a short time are ubiquitously observed
For example, individuals can form a new flock after adjusting their states in a short time when they are disturbed by the external environment
Summary
In the last few years, the cooperative control of self-propelled agent systems has attracted considerable attention, mainly due to its broad range of potential applications including formation control [1], attitude alignment [2], and target tracking [3]. Ji et al [20] studied the finitetime and fixed-time synchronization by establishing a new finite-time and fixed-time theorems For another relative interesting results on finite-time problems, we refer to [21,22,23,24,25,26,27,28,29,30,31] and therein references. Unlike the results in [32, 33], in which flocking is achieved in a finite-time which is depending on the initial states of network agents, we investigate the fixed-time flocking and estimate the upper bound of the settling time which is merely depending on parameters.
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