Scaled Group Consensus Of Multi-agent Systems

In recent years,the consensus of multi-agent systems has become a hot research topic and plays an important role in many fields.By designing various types of control protocols,the researchers make all individuals in multi-agent systems finally achieve consensus or group consensus.At present,there have been abundant results on the consensus of the first-order and second-order multi-agent systems.While the theory of highdimensional systems and group consensus problems need to be further improved.Therefore,this thesis focuses on scaled group consensus of multi-agent systems.Several types of definitions of scaled group consensus are presented and some relevant control protocols are designed.Then we combine the consensus of high-dimensional systems and scaled group consensus.Based on the graph theory,the matrix theory,the special matrix theory and the stability theory,the conditions on group consensus are proposed and proved strictly.Several simulation examples are presented to manifest the accuracy of the relevant theoretical results.The main contributions are as follows:1.For the first-order multi-agent systems,the definition of scaled group consensus of the first-order systems is proposed under the continuous-time condition.The firstorder control protocol is designed.The judging theorem of the first-order scaled group consensus is provided and proved in detail by using the matrix theory.Some specific simulation examples are presented to manifest the correctness of the relevant theoretical results.2.This thesis generalizes scaled group consensus problems of the first-order systems to the second-order systems.The definition of scaled group consensus problems of the second-order systems is proposed under the continuous-time condition.The secondorder control protocol is designed.The judging theorem of the second-order scaled group consensus is provided and proved in detail by using the matrix theory.Several specific simulation examples are presented to manifest the correctness of the relevant theoretical results.3.This thesis combines high-dimensional consensus and scaled group consensus,investigates scaled group consensus problems of the high-dimensional systems under the discrete-time and the continuous-time conditions respectively.The definitions of scaled group consensus of the high-dimensional systems are proposed.The high-dimensional control protocols are designed.The judging theorems of high-dimensional scaled group consensus are provided and proved in detail by using the matrix theory,the special matrix theory and the stability theory.Some specific simulation examples are presented to manifest the correctness of the relevant theoretical results.