On Multi-Consensus And Multi-Tracking Of Mulit-Agent Systems

In the national economy and social development, cooperative control of multi-agent systems has extensive application prospects, such as formation control of autonomous underwater vehicles, autonomous configuration of sensor networks, and attitude control of man-made satellites. When multiple agents accomplish a complex task cooperatively, the states of agents converge to several consistent values at some stages due to different task distributions or changing situations. The key problem of cooperative control is to design suitable distributed algorithms. Multi-consensus and multi-tracking of second-order multi-agent systems are investigated, and distributed algorithms are designed considering the practicability, time complexity, and space complexity of algorithms. The research has not only the important theory significance, but also the practical application value to guide engineering problems. The main work is as follows.A multi-consensus problem is proposed in multi-agent systems, and the impact factor of intelligence is introduced to describe the interaction mechanisms among agents, including competition, abstention, and cooperation. Three distributed linear protocols and a unified distributed impulsive protocol are designed with the states of itself and partial neighbor agents. Only position sampled data is required in the distributed impulsive protocol. The behaviors of multi-consensus are discussed for second-order multi-agent systems with bounded velocities of agents. Necessary and sufficient conditions are obtained to achieve each multi-consensus. Feedback gains and sampling period are related with the real and imaginary parts of the eigenvalues of the control matrix; the sampling period may be restricted simultaneously by a positive upper bound and a positive lower bound.Taking the practical application of impulsive control in multi-agent systems into consideration, multi-consensus of second-order discrete-time multi-agent systems is studied under rectangular wave control. In the Lebesgue-Stieltjes measure, based on the principle that the integration of rectangular wave protocol equals to the integration of impulsive protocol for solving multi-consensus problem within a sampling period, three rectangular wave protocols are proposed. Necessary and sufficient conditions on control parameters are obtained to achieve three categories of multi-consensus. Noticing that the vertices of multi-agent network have differences in intelligence, we introduce a concept of intelligence degree. Multi-consensus of second-order continuous-time multi-agent systems with hybrid intelligence is investigated without grouping of multi-agent networks. Three switched impulsive protocols are proposed using either position data or velocity data at sampling instants. Necessary and sufficient conditions on digraph topology are presented to select proper feedback gains and sampling period. The finial states of multi-consensus are determined analytically.The tracking control with a time-varying reference velocity usually adopts a variable structure approach. However, it is hard to handle the tracking problem using sampled data. For the multi-tracking problem of multi-agent systems via sampled-data control, a distributed impulsive protocol is proposed, in which only position sampled data of the agents and the desired trajectories are utilized. Two cases with the constant and time-varying desired velocity are discussed respectively. Necessary and sufficient conditions are obtained to achieve uniform multi-tracking and bounded variable multi-tracking, and the ultimate tracking error of bounded variable multi-tracking can be controlled by adjusting sampling period.For multi-agent systems with different uncertain nonlinear dynamics and external disturbances, a robust multi-tracking problem is studied for second-order continuous-time heterogeneous multi-agent systems. A distributed impulsive protocol is proposed, in which the information of desired trajectories is needed at sampling instants. The error system for achieving multi-tracking is decomposed into two impulsive systems with vanishing perturbation and nonvanishing perturbation, respectively. By introducing a nominal mpulsive system, the convergence of error system is analyzed. The result shows that the solution of error system is eventually within a bounded closed set.