Stability Analysis Of Swarms With A Pair Of Chains Communication Topology

In this paper, characteristic of Swarm Intelligence and stability analysis of one-dimensional and M-dimensional asynchronous swarm are discussed. Stability is a basic qualitative property of swarm since if it is not present, then it is maybe impossible for the swarm to achieve any other group objective. There are three main parts in this paper. The first is the instruction on Swarm Intelligence, which includes simple agents, complex cooperative behavior, simple intelligence properties of each agent and cooperative emergence behavior by direct and indirect communication. These biological systems have good self-organize, self-reconstruction and tolerance. Emergence behavior is one of the most prominent qualities, which is alternative means of complexity system research.The second is stability analysis of one-dimensional asynchronous swarm. The cohesi-veness of the swarm is characterized as a stability property. The models of swarm member and one-dimensional asynchronous swarm are defined. Each member senses the neighbor distance via both neighbor position and proximity sensors and makes decisions for movements according to the difference between the sensed distance and the comfortable distance via its "decision-making" mechanism. A discrete-time discrete event dynamical system aproach is used for research in this part. It is proved that one-dimensional asynchonous swarm can achieve convergence, where intermember communication channels are less than perfect.The third is that a model and stability analysis of M-dimensional asynchronous swarm with a pair chain communication topology is studied, which has more practical applications in engineering systems. In this part, each member only communicates with fixed neighbors. Each member has proximity sensor and neighbor position sensor and updates its position through position of reference member by neighbor position sensor. It is proved that the swarm can achieve stability and make two communicating neighbors be of a comfortable distance, even in the presence of sensing delay and asynchronism. The conclusion is obtained that the research in this paper is similar to the studies of platoon stability in intelligent transportation system.