Research On Multi - Agent Distributed Consistency With Input Noise

In recent years, with the development of artificial intelligence and Internet of Things, multi-agent systems have received increasing attention especially in robots network, urban traffic, distributed computing, neural networks robots and wireless networks, etc. The research results show multi-agent systems can perform many complex control tasks.In the distributed multi-agent systems, consensus means that the state of each agent achieves consensus by communication and collaboration among them. The research focuses of distributed consensus are convergence, convergence speed, communication protocol optimization, network structures, event triggers and constraint optimization. In practice, due to nonideal external conditions and equipments, quantization coding and noise must be considered.Consequently, this paper analyzes distributed consensus with input noise in multi-agent systems. We consider an undirected network which can be presented by a first order difference equation, and we use few equations to portray constraints,quantization and coding rules.Firstly, this paper discuss the multi-agent systems with a fixed topology. We assume that the limited input noise is uniformly distributed with zero expectation value,which is independent of the values of agents. Because noise is a random variable, after several iterations, the values of agents turn into a stochastic process, which may not eventually reach consensus. We get the network can achieve consensus with some constrain conditions, and the final state is also a random value. Finally, we analyze the statistic features and convergence rate of this system.Secondly, we consider the multi-agent systems with a random topology. Because of the random system structrue, its corresponding Laplacian matrix is also time-varying.It is easy to know the process is a markov process. First of all, we assume that the quantization is unbounded to avoid quantization saturation. In the markov process, for the sake of randomizing the quantization errors, we add a dither satisfying the Schuchman conditions. We prove that the average states sequence is a second-order bounded martingale process, which is used to reach the convergence in probability. Forbounded quantization, we show that we can increase the consensus probability by designing the quantization and parameters restrictive conditions. Then we give the functions about the consensus probability and parameters in detail.