Observer‐Based Time‐Varying Group Formation‐Containment Tracking for Input‐Saturated Multi‐Agent Systems

ABSTRACT This paper investigates the time‐varying group formation‐containment (TVGFC) tracking problem for multi‐agent systems (MASs) with input saturation, and simultaneously accounts for unknown control inputs. The system consists of three types of agents divided into different subgroups: Formation leaders, followers, and tracking leaders. These agents are respectively responsible for providing macroscopic motion references, achieving sub‐formation tracking, and converging to the convex hull within their corresponding subgroups. Firstly, by adjusting the structure of the Laplacian matrix that characterizes inter‐agent interactions, the subdivision of all agents into subgroups is achieved. Then, an observer‐based TVGFC tracking control protocol and a feasible constraint for formation tracking are proposed. Theoretical analysis confirms that the proposed protocol ensures the achievement of the desired TVGFC tracking. Furthermore, a continuous control protocol is designed to suppress chattering resulting from the unknown input. The proposed protocol guarantees that the errors remain ultimately bounded, which can be asymptotically driven into an arbitrarily small neighborhood of zero. Ultimately, a numerical simulation validates the effectiveness of the proposed control scheme.