Time-varying group formation-tracking control for general linear multi-agent systems with switching topologies and unknown input

Time-varying group formation tracking problems for general linear multi-agent systems with unknown control input and switching topologies are studied. There are two kinds of agents, leaders and followers. Leaders with unknown control input can generate unpredictable and maneuverable trajectories. Followers accomplish macroscopic moving guided by single or multiple leaders of respective subgroups and keep desired time-varying sub-formations simultaneously. Agents are assigned in groups and interactions within or between groups both exist owning to the design of Laplacian matrix. First, the time-varying group formation tracking problem is described and group division is analyzed through adjustment of properties in Laplacian matrix. Then the control protocols based on neighboring interaction relationships are introduced. Influence of unknown control input from leaders can be handled and information is delivered effectively so that followers can accomplish expected formations. An algorithm is given to determine control parameters and the formation tracking feasible constraint is presented. Next the stability of the multi-agent system with group division is proved, which means the general linear multi-agent system can accomplish time-varying group formation tracking with unknown control input and switch topologies under designed protocols. At last, a numerical simulation is given to verify the effectiveness of presented theoretical results.