Consensus Control For Discrete-time Multi-agent Systems With Switching Topology

In recent years, with the actual needs of the application and the development ofscience and technology, cooperative control of multi-agent system in the world hasattracted a great number of researchers with rather diverse background such asbiology, physics, mathematics, information science, computer science. Due to therapid development of information and computing, the multi-agent system has beenwidely applied to many fields, such as cooperative control of mobile robots,unmanned aerial vehicles, autonomous formation flight formation, control ofmulti-sensor, non-formation of cooperative control problems, such as the taskassignment, payload transport, air traffic control, coverage control of mobile sensornetwork, the national economy and defense, military and other high-tech engineering.It has demonstrated a very broad application prospects.In this paper, we mainly consider a multi-agent system in the state ofdiscrete-time and high-dimensional linear coupling dynamics. Due to the limitednature of the system communications and sensing, a random switching andtime-varying undirected-network topology is modeled to simulate the real multi-agentsystem, and a output feedback controller which is based on the neighbors is designedto solve the consensus problem of the switching network of autonomous individuals.By using graph theory, matrix theory, common Lyapunov function method, andH_∞control theory, applying LMI and the Riccati equation to solve the output feedbackmatrix, we resolve the consensus problems of the multi-agent system in the state ofhigh-dimensional linear coupling dynamics.The main results obtained in this paper are as follows:In this paper, we consider that stability of the multi-agent system with theundirected switching topology is free from noise and other disturbances. We constructa control protocol based on local information, translate the multi-agent system intosubsystem’s Schur stability problem by using the theory of matrix, and propose theimproved discrete-time algebraic Riccati-equation which can be used to solve LMIand obtain the feedback gain matrix. Finally, validity of the theoretical results is illustrated by simulating examples.We study theH_∞control problem of the multi-agent system with the undirectedswitching topology, which is accompanied by noise and other disturbances. Wedesign output feedback protocol to solve the consensus problem of multi-agent systembased on the neighbors’ information, obtain Schur stability conditions of multi-agentby usingH_∞control theory in the presetH_∞performance indicators, and at thesame time get the value of the feedback matrix by solving LMI.We investigateH_∞dynamic output feedback consensus control problems fordiscrete-time multi-agent system with the undirected switching topology, which isaccompanied by noise and other disturbances. The design is based on the dynamicoutput feedback control protocal of local information, and apply public Lyapunovstability theory andH_∞control theory to solve the consensus problem of multi-agentsystem. In the presetH_∞performance indicators, we apply control theory, combinewith the LMI and solve it, and at last get the Schur stability conditions of multi agentsystem.