Distributed Time-Varying Formation Control for Linear Swarm Systems With Switching Topologies Using an Adaptive Output-Feedback Approach

Fully distributed time-varying formation (TVF) control problems are addressed in this paper using an adaptive output-feedback approach for general linear swarm systems with fixed and switching topologies. In contrast to the earlier results on formation control problems, the general linear swarm system can achieve the predefined TVF using only local output information and independent of the Laplacian matrix associated with the communication topologies. The implementation cost of calculating the global information and requiring full state information is avoided when achieving the desired TVF. First, a node-based TVF control protocol is constructed via dynamic output feedback for the case with fixed communication topology, where adaptive-based coupling weights are introduced to eliminate the dependence on the global information about the topology. Then an algorithm is presented to determine the gain matrices in the node-based adaptive TVF control protocol, and a feasible formation constraint is provided. The stability of the algorithm is proved based on the Lyapunov theory. Furthermore, under the case of switching communication topologies, an edge-based TVF control protocol is constructed with dynamic output feedback and an adaptive law for adjusting the coupling weights among agents. A sufficient condition is derived using the common Lyapunov theory for general linear swarm systems to achieve the predefined TVF satisfying the feasible formation constraint. Two numerical examples are presented to illustrate the theoretical results.