Synchronization-Based Guaranteed-Performance Formation Design for Swarm Systems

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.

Consensus Problem of High-Order Multiagent Systems with Time Delays

In this paper, we consider the consensus problem of high-order multiagent systems on both fixed and switching interaction topologies with time delays. A neighbor-based protocol is presented, under which we prove that the state errors converge to zero asymptotically if there is a solution to a given Riccati inequality. The proof of our theorem is shown in time domain based on a Lyapunov approach. A numerical example is introduced to indicate the correctness of our analysis.

Oscillation Criteria for Third Order Differential Equations with Functional Arguments

In this paper, we consider the third order differential equations with functional arguments by using Riccati inequality