Formation control for networked multiagent systems with a minimum energy constraint

Minimum-energy formation achievement problems for networked multiagent systems are investigated, where information networks with leaderless and leader-follower structures are respectively addressed and information networks are randomly switching. The critical feature of this work is that the energy constraint is minimum in the sense of the linear matrix inequality, but limited-budget control and guaranteed-cost control cannot realize a minimum-energy formation. Firstly, the leaderless minimum-energy formation control problem is converted into an asymptotic stability one via a nonsingular transformation and state space decomposition, and based on linear matrix inequality techniques, sufficient conditions for analysis and design of leaderless minimum-energy formation achievement are proposed, respectively, which can be solved by the generalized eigenvalue method. Then, main results of minimum-energy formation achievement of leaderless networked multiagent systems are extended leader-follower networked multiagent systems, where the asymmetric property of the leader-follower information network is well dealt with by two nonsingular transformations. Finally, two simulation examples are shown to verify the main results for minimum-energy formation achievements of leaderless and leader-follower networked multiagent systems, respectively.