Research On Distributed Formation Control Of Multi-agent Systems Based On LMI

In recent decades,the research of multi-agent systems has attracted more and more attention from scholars at home and abroad,the main reason is that multi-agent systems can solve complex and difficult problems that can not be solved by a single agent through cooperation and negotiation among them,and multi-agent systems are widely used in military,aerospace and many other fields.Therefore,the research on multi-agent systems is of great significance both in theory and in practical engineering applications,in this paper,the distributed formation control of multi-agent systems with nonlinear characteristics is mainly studied.The main contents of this paper are as follows:(1)Formation control of multi-agent systems with the same time-varying delaysThe formation control problem for nonlinear multi-agent systems is addressed.Under the fixed topology,assuming the communication delays between agents are the same,a suitable distributed fornation control protocol is proposed and analysed in theory.Based on the knowledge of the matrix,the stability of the systems is analyzed by model transformation and Lyapunov stability theory.Then we give the sufficient conditions for multi-agent systems to realize the stability of formation control by using the method of linear matrix inequality(LMI),so that the multi-agent systems can effectively realize the formation control.Similarly,under the switching topology,a similar method is used to research the formation control for the second order nonlinear multi-agent systems.(2)Robust H_? formation control of multi-agent systems with the same time-varying delaysThe robust H_? formation control for multi-agent systems with time-varying delays is addressed.In the case of fixed topology,firstly,a suitable distributed formation control protocol is designed without considering external disturbances and uncertain parameters.Constructing the Lyapunov functional and based on the knowledges of inequality and linear matrix inequality,the formation control problem of multi-agent systems is solved.Secondly,under the condition of external disturbance and uncertain parameters,the robustH_? formation control of multi-agent systems is studied,and the sufficient conditions for solving the formation control problems are given.Similarly,in the switching topology,a similar method is used to research the robustH_? formation control.That is,under the distributed control protocol,the multi-agent systems can not only achieve the desired formation,and the position and speed of the multi-agent systems can be consistent,but also meet theH_? performance index.(3)Formation control of multi-agent systems with multiple time-varying delaysThe formation control for multi-agent systems is studied under the condition that the time-varyings between agents are different.For the topologies of the multi-agent systems are both fixed and switched,we design the distributed control protocol with multiple time-varying delays,with the help of graph theory and other related knowledges,the formation control protocol is theoretically analyzed by selecting Lyapunov function,so the sufficient conditions for solving the formation control problem of the multi-agent systems are obtained,and the multi-agent systems can achieve and maintain the desired formation.