Formation Tracking for High-Order Time-Invariant Swarm Systems with Limited Energy and Fixed Topologies

Abstract

The current paper investigates design and analysis problems of formation tracking for high-order linear time-invariant swarm systems, where communication topologies among agents have leader-following structures and the whole energy supply is limited. Firstly, the communication topology of a swarm system is depicted by a directed graph with a spanning tree, where the communication channels from the leader to followers are directional and the communication channels among followers are bidirectional, and a new formation tracking protocol with an energy integral term and a given upper bound is proposed to achieve formation tracking with the limited energy. Then, sufficient conditions for time-varying formation tracking design and analysis with the limited energy are presented, respectively, which include two/three linear matrix inequality constraints associated with the maximum and minimum nonzero eigenvalues of the Laplacian matrix of a communication topology. Especially, time-invariant formation tracking criteria are further deduced. Finally, two numerical examples are revealed to verify main theoretical conclusions.

Adaptive guaranteed‐performance consensus for high‐order nonlinear multi‐agent systems with switching topologies

“…Two switching topologies with jointly‐connected and connected were considered in Reference 14, which enable linear MASs to achieve consensus on guaranteed cost. Reference 15 analyzed the time‐invariant formation‐tracking consensus problem for high‐order linear systems and took into account the limitation of each agent's energy supply to complete the guaranteed‐performance formation tracking consensus. A control protocol with guaranteed‐cost consensus was designed in Reference 16, to implement guaranteed‐performance consensus for MASs with time‐varying delays.…”