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Time-varying formation control protocol design and analysis problems for the second-order discrete-time multi-agent systems with directed interaction topology and communication delay are investigated. A local information-based distributed protocol is designed by utilizing the delayed state information of neighbors. Through system decomposition and stability analysis, an explicit description of the feasible time-varying formation set is given. Necessary and sufficient conditions for the systems with the directed topology and communication delay to achieve time-varying formation are obtained, which are related to the topology of the interaction graph and the feasibility of the predefined formation. Necessary constraints on the gain parameters and the sampling period are proposed, so as to guide the design of parameters in the protocol. The numerical simulation results indicate that the protocol can steer the agents to accomplish the desired time-varying formation and effectively tolerate the relatively large bounded communication delay. Outdoor experiment with quadrotors is presented to demonstrate the effectiveness of the obtained theoretical results with one sampling period delay.INDEX TERMS Multi-agent systems, consensus control, time-varying formation, directed topology, communication delay.

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In this paper, the angle-of-arrival (AOA) measurements are adapted to locate a target using the UAV swarms equipped with passive receivers. The measurement noise is considered to be target-to-receiver distance dependent. The Cramer-Rao low bound (CRLB) of the AOA localization is calculated, and the optimal deployments are explored through changing angular separations and distances. Then, a distributed collaborative autonomous generation (DCAG) method is proposed based on the deep neural network (NN). The off-line training and on-line application rules are applied to generate the optimal heading angles for the UAV swarms in the AOA localization. The simulation results show that through the DCAG method, the generated heading angles for UAV swarms enhance the localization accuracy and stability. INDEX TERMS AOA localization, distributed collaborative autonomous generation (DCAG), Cramer-Rao low bound (CRLB), deep neural network (NN).

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