Abstract
We consider multiagent consensus problems in a decentralized fashion. The interconnection topology among the agents is switching and directed. The agent dynamics is expressed in the form of a double‐integrator model. Two different cases are considered: one is the leader‐following case and the other is the leaderless case. Based on graph theory and the common Lyapunov function method, some sufficient conditions are established for the consensus stability of the considered systems with the neighbor‐based feedback laws in both leader‐following case and leaderless case, respectively. As special cases, the consensus conditions for balanced and undirected interconnection topology cases can be established directly. Finally, two numerical examples are given to illustrate the obtained results.
Highlights
In recent years, the coordination problem of multiple autonomous agents has drawn an increasing attention
The coordination problem of multiple autonomous agents has drawn an increasing attention. It is because there are many applications of multiagent systems in many areas including cooperative control of unmanned air vehicles, flocking of birds, schooling for underwater vehicles, distributed sensor networks, attitude alignment for cluster of satellites, collective motion of particles, and distributed computations 1–5
The main purpose of this paper is to develop a decentralized control strategy to reach the global consensus of the multi-agent systems under directed switching interconnection topology among the agents
Summary
The coordination problem of multiple autonomous agents has drawn an increasing attention. The main purpose of this paper is to develop a decentralized control strategy to reach the global consensus of the multi-agent systems under directed switching interconnection topology among the agents. We can obtain consensus conditions directly for the multi-agent system with undirected and balanced switching interconnection topology. For double-integrator model, we construct a counterexample to show that the jointly connected condition may not guarantee that the multi-agent system achieves consensus, which implies that the proposed globally reachable convergence condition may be moderatable and acceptable. Some results on the consensus stability are obtained for the multi-agent system with fixed and varying interconnection topologies in the leader-following case, while, the leaderless case is studied. For symmetric matrices A, λmin A and λmax A represent the minimum and maximum eigenvalue of A, respectively. denotes the Euclidean norm. ⊗ denotes the Kronecker product, which satisfies 1 A ⊗ B C ⊗ D AC ⊗ BD ; 2 if A ≥ 0 and B ≥ 0, A ⊗ B ≥ 0
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