Research On Evolutionary Analysis And Pattern Control Of Collective Dynamical Systems

The main feature of collective dynamical systems(CDSs)is that simple individual intelligence and pairwise interaction can stimulate the emergence of complex group behaviors.The relevant theory and techniques are considered to have a wide range of applications in the field of formation control of unmanned systems,smart grid and others.The research difficulty of CDSs lies in the fast evolution of aggregation and dispersion of group patterns,the determination of the individual decision-making mechanism and the interaction mechanisms.Since the complicated evolution process has never stopped,therefore,it is difficult to ensure which stable configuration the group will eventually form.In this thesis,in-depth studies have been conducted on the behavioral characteristics,individual interaction rules,individual decision-making mechanism and the evolutionary regulation mechanism of collective configuration in CDSs,and the following research results have been achieved:The spatiotemporal properties of CDSs have been studied.By using the high-resolution GPS data of homing flight of pigeon flocks,an exact switching hierarchical mechanism is revealed.It is found that a stable long-range leader exists in homing flight of pigeon flocks,and the influence of spatial distribution on identity switching.Further studies have revealed the relationship among the decision sequence of CDSs,the spatial location and individual dominances.An analysis method of interaction mechanism of CDSs based on statistical mechanics has been proposed.By analyzing the data of pigeon flock flights,it is found that the communication of natural biological groups is not carried out constantly.An intermittent way exists,which effectively reduces communication energy consumption.Moreover,to ensure the aggregation of group members,the communication network of pigeon flocks is not always connected.On the time scale,there is almost no connected communication network at a single moment,and the union of a few frames of communication networks is more likely to be connected.It provides the biological support for the topological assumptions in multi-agent systems and provides theoretical guidance for the way of the network connectivity mechanism adopted in industrial unmanned systems.An analysis method of interaction mechanism of CDSs based on machine learning has been proposed.To reveal the interaction mechanism among individuals,the sparse Bayesian learning method is used to analyze the free flight data of pigeon flocks.It is revealed that there exists a significant positive correlation between the interaction frequencies of individuals and the reciprocal of the metric distance.Note that it is not the closer the individuals are,the stronger the communication is.In the case of short pairwise distance,the main interaction between individuals is repulsive force which does not show the alignment of velocities and positions.When the distance is greater than this threshold,interaction frequency decreases linearly with distance growing larger.At the same time,this work reveals that individuals in the flocks intertwine with each other on the left and right sides of the flight direction,which shows obvious anisotropy.Decision-making strategy of CDSs has been explored.Based on Hamiltonian dynamics,the energy evolution from individual level to group level is revealed from another perspective of classical mechanics.Furthermore,the internal symmetric decision-making of pigeon flocks is revealed by combining the mechanism of group coordination.To study the predictability of CDSs,we collect and investigate a comprehensive data set of human activities of using mobile terminations to surf the internet on large geographical scales.Quantitative analysis shows that the spatiotemporal characteristics of human behavior network indicates scale-free rules with power-law distribution and exponential truncation,and the clustering coefficient tends to be fixed.To further study its information entropy and high predictability,it is found that human behavior is non-Markovian and can be characterized by the random walk model with preferential return and exploration tendency.A method of regulating pattern phase transitions of CDSs has been proposed.The Vicsek-minimum model based on velocity alignment reveals the very similar phase transitions of water in the solid-liquid-gas phase switches.As individual field of view increases,the system exhibits a transition from “gaseous” to “crystalline” to “liquid”;more interestingly,with the further expansion of field of view,a new “vortex” state appears;as individual avoidance trend strengthens,the “vortex” state splits into “solid”,“hollow”,and “single ring” sub-states.This work provides a new insight for understanding the evolution of CDSs.At last,this thesis summarizes the entire research,and proposes a prospect for further research on the evolutionary analysis and configuration control of CDSs and the future development direction.