Abstract
Guaranteed-performance formation control for swarm systems with the second-order dynamics is investigated based on the synchronization control strategy. Firstly, a new formation protocol is presented, where the weights of connected edges are adaptively regulated and the performance constraint is imposed. Then, on the basis of the Riccati inequality, sufficient conditions for synchronization-based guaranteed-performance formation are proposed, and an explicit expression of the guaranteed-performance cost is shown, where it is fully distributed to design gain matrices of the formation protocol in the sense that it is independent of global information of swarm systems. Moreover, the whole motion of a swarm system is determined, which is associated with initial states of all agents and formation control vectors. Finally, two numerical examples are shown to demonstrate theoretical conclusions, where the static whole motion and the dynamic whole motion are considered, respectively.
Highlights
A lot of researchers paid their attention to distributed coordinated control of swarm systems since they have wide foregrounds in many fields, such as animal flocking [1, 2], network synchronization [3,4,5,6,7,8], and formation of multiple intelligent agents [9,10,11,12,13]
It was pointed out that the virtualstructure approach is centralized, and the behavior-based approach cannot be analyzed by establishing accurate models and implementing rigorous deduction it is distributed. e synchronization-based formation control approach is valid to realize specific structures by designing formation control vectors, where some coordinated variables in practical swarm systems are chosen and these errors between coordinated variables and formation control vectors are required to achieve synchronization. e synchronization-based formation control approach can overcome some drawbacks of the virtual-structure approach and the behavior-based approach, and it can establish formation in a distributed mode
By constructing Lyapunov functions with the adaptively regulated weight terms, the translation adaptive method is proposed to eliminate the impacts of nonzero eigenvalues, and sufficient conditions for synchronization-based guaranteed-performance formation are proposed, which are fully distributed since they are not associated with global information of swarm systems
Summary
A lot of researchers paid their attention to distributed coordinated control of swarm systems since they have wide foregrounds in many fields, such as animal flocking [1, 2], network synchronization [3,4,5,6,7,8], and formation of multiple intelligent agents [9,10,11,12,13]. As far as we know, the synchronization-based guaranteed-performance formation design problem for swarm systems with the fully distributed control strategy is still not comprehensively studied. Is paper investigates a fully distributed strategy to realize synchronization-based guaranteed-performance formation design for swarm systems. By constructing Lyapunov functions with the adaptively regulated weight terms, the translation adaptive method is proposed to eliminate the impacts of nonzero eigenvalues, and sufficient conditions for synchronization-based guaranteed-performance formation are proposed, which are fully distributed since they are not associated with global information of swarm systems. Synchronization-based guaranteed-performance formation criteria are fully distributed; that is, the gain matrix design is independent of the global information of communication networks of swarm systems.
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