Distributed Adaptive Control Of The Multi-agent Systems

The consensus of multi-agent is ubiquitous in nature, such as flocking of birds, schooling of fish, the migration of the geese, etc. Nowadays, the consensus problem of multi-agent systems is an important developing direction of the control theory due to the broad application of the consensus in biological systems, sensor networks, Unmanned Air Vehicle(UAV) formations, robotic teams, underwater vehicles, etc. The main content of this article are the consensus of second-order nonlinear multi-agent system and the heterogeneous multi-agent, in which the position and velocity have independent topology.Firstly, this paper presents some theories that the analysis of the multi-agent systems needed. Because the transmission of information between agents can be represented by the topology, so knowledge of the graph theory is very helpful to the theoretical analysis. As the theoretical analysis is carried out through the establishment of Lyapunov function analysis, it is necessary to understand what the Lyapunov stability is.Secondly, we consider the general second-order nonlinear multi-agent system which has unknown time-varying topology connection coupling weights for each edge and each node. So we adopt an adaptive approach, constructing suitable Lyaunov function, using graph theory and Schur Complement Lemma, then after La Salle Invariance principle, we can obtain the sufficient conditions to get the consensus of the multi-agent systems. Finally, the effectiveness of the proposed method is illustrated with some simulation examples. The key part and difficulty lies in finding a suitable Lyapunov function, and then design adaptive protocol based on the edge and nodes.Finally, our research focuses on the heterogeneous multi-agent systems. Part of the agents in the system has second-order nonlinear dynamic, while the other part only have position information and the speed information is unknown. Here we adapt adaptive methods to deal with the time-varying coupling weights for each edge and each node. Then choose an appropriate Lyapunov function to get the sufficient condition of the system consensus. At last, we use computer to do numerical simulation to prove the effectiveness of the theory. As part of the agent speed information is unknown to us, this increases the difficulty to design the adaptive protocol which is based on the edges and nodes.