Research On The Fixed-time Consistency Problem Of The Second-order Multi-agent System Based On The Directed Graph

In recent years,the consensus problem for multi-agent systems has became a focal point and has appeared as a challenging subject in the field of control.Through in-depth research,more methods are proposed.The problem of fixed-time consensus protocols for second-order multi-agent systems with directed communication topol-ogy becomes a hot topic increasingly.Based on the Lyapunov stability theory,linear matrix inequality,sliding mode and the structures and properties of the graph.The main work of this paper is as follows:In the first chapter,we first indicate the research process and status of the consensus problem for multi-agent systems.Then,to derive the desired result suc-cessfully,we introduce some basic knowledge about graph theory and matrix theory.In the second chapter,we study the problem of fixed-time consensus protocol-s for second-order multi-agent systems.Firstly,the network model of convergence problem is given according to graph theory and the relationship between agents to be studied.Then,we propose a suitable control protocol.By employing the Lyapunov stability theory,we make the system finish convergence at a fixed time.Finally,we prove our theorem with an example.In the third chapter,we consider the problem of fixed-time tracking protocols for second-order multi-agent systems with directed communication topology.Firstly,under the premise of the second chapter,we add a leader to form the tracking prob-lem model.Then,we propose a suitable control protocol.By using the Lyapunov stability theory and sliding mode,we make the system finish convergence at a fixed time.Finally,we prove our theorem with an example.Finally,the fourth chapter summarizes the research work of this dissertation and provides some trends for the future research.