Distributed formation for interconnected networks with minimum energy restriction and interaction silence

The minimum-energy formation strategy for interconnected networks with distributed formation protocols is persented, where the impacts of the total energy restriction and the interaction silence are analyzed, respectively. The critical feature of this article is that the distributed formation and the minimum-energy restriction are realized simultaneously, and the total energy restriction is minimum in the sense of the linear matrix inequality. However, the guaranteed-cost formation strategy and the limited-budget formation strategy cannot guarantee that the energy restriction is minimum. Firstly, sufficient conditions for minimum-energy-restriction formation without the interaction silence are proposed, which can be solved by a specific optimization approach in terms of the linear matrix inequality, and the formation whole motion trajectory is determined, which is closely related to the average of the initial states of all agents and formation control vectors. Then, minimum-energy-restriction formation criteria for interconnected systems with the interaction silence are proposed by introducing two inhibition parameters and the interaction silence rate. Finally, two simulation examples are performed to illustrate the effectiveness of theoretical analyses.