Quantized Consensus Problem Of Networked Multi-Agent Systems With Finite Bit Rate

During the past decade,the consensus problem of multi-agent systems has attracted more and more attention,due to its outstanding distributed property and wide applica-tion backgrounds.As the scale of the multi-agent systems increases,agents have to communicate with each other utilizing the wireless communication network.However,in most practical scenarios,due to the constraints on sensor cost,communication band-width and energy budget,information can only be transmitted at discrete time instants and has to be quantized into digital signals with only finite number of bits before trans-mission.This implies that most existing results can not be applied directly.Therefore,the consensus problem of networked multi-agent systems has also been widely stud-ied as one of the most important topics of this field.Generally speaking,this problem is concerned with designing encoding-decoding policies of local information exchange and interaction rules among agents such that all agents in the system make an agreement on certain specific physical quantity ultimately.Further,to reduce the heavy burden on the communication network,it is expected that the necessary bit rate of the multi-agent system can be as low as possible.This requires to design dynamic quantization strategy with only finite bits.However,due to the cooperative nature of the multi-agent systems,it is almost impossible for each agent to acquire the control in put of its neighbors.This brings a huge challenge on the synchronization of quantization ranges,which is of great importance to the dynamic quantization.In this dissertation,based on existing research works,we mainly investigate the quantized consensus problem of networked multi-agent systems with finite bit rate.The main contributions of this dissertation are as follows.First of all,we propose a dynamic encoding-decoding policy based on internal saturation function.To guarantee the synchronization of quantization ranges between neighboring agents,traditional methods commonly estimate the state of the whole multi-agent system utilizing some global information,and predict the control input of each agent.However these global information are hard to get in most situations.Instead,we introduce internal saturation function into the controller of each agent such that the con-trol input is constrained within a scope that can be known in advance.With the help of this public information,neighboring agents can update their corresponding quantization ranges at the same extent and implement synchronization.Then,we propose a quantized consensus protocol based on constant internal sat-uration value with finite bit rate,which is built upon the basis of the aforementioned dynamic encoding-decoding policies.Under any given constant saturation value and parameters satisfying certain conditions,the multi-agent system can achieve approxi-mate consensus with only finite bit rate.The bit rate can be as low as 1 bit per step.In addition,we analysis the unavoidable disturbance of bounded additive noise and the situation with unknown network topology.By modifying the consensus protocol,the approximate consensus can still be guaranteed for the multi-agent system without re-quiring more bits.Further,we propose a quantized consensus protocol based on dynamic internal saturation value with finite bit rate.Under time-varying internal saturation value,which is in the exponential and hybrid form respectively,it can be seen that the quantization error of each agent converges to zero as time goes on.Then the new quantized consensus protocols can guarantee the achievement of more accurate asymptotic consensus for the multi-agent system without requiring more quantization bits.In addition,we an alysis the situation where the system is affected by the bounded additive noise and estimation mismatch.Under two specific circumstances we model the estimation mismatch by giving the expressions of its upper bounds,and prove that the multi-agent system can achieve consensus in the input-to-state sense with finite bit rate.Finally,with the help of event triggering mechanism,we present a new approach to deal with the quantized consensus with finite bits.Traditional methods commonly choose a fixed period,and only at the beginning of each period do the agents sample,quantize,encode and send out their states.However this setting may cause unneces-sary waste of communication resources.We propose a dynamic quantization strategy based on event triggering that each agent quantizes and sends information out only when some pre-defined events occur.By extracting useful information from the triggering instants that are ofter ignored,the new quantized consensus protocol acquire lower bit rate than those of most state-of-the-art time-triggered strategies.In addition,we modify the consensus protocol to handle the network-induced delay.It can be guaranteed that asymptotic consensus can still be achieved.We also present a method to compute the maximum tolerable network delay under given conditions.