Formation-containment control problems for multiple multirotor unmanned aerial vehicle (UAV) systems with directed topologies are studied, where the states of leaders form desired formation and the states of followers converge to the convex hull spanned by those of the leaders. First, formation-containment protocols are constructed based on the neighboring information of UAVs. Then, sufficient conditions for multi-UAV systems to achieve formation-containment are presented. An explicit expression to describe the relationship among the states of followers, the time-varying formation for the leaders and the formation reference is derived. It is shown that the states of followers not only converge to the convex hull formed by those of leaders but also keep certain formation specified by the convex combination of the formation for the leaders. Moreover, an approach to determine the gain matrices of the formation-containment protocol is proposed by solving an algebraic Riccati equation. Finally, a formation-containment platform with five quadrotor UAVs is introduced, and both the simulation and experimental results are presented to demonstrate the effectiveness of the obtained results.

This paper studies the time-varying output formation (TVOF) tracking problems for heterogeneous linear multi-agent systems with a nonautonomous leader on directed topologies, where the dynamics of the agents can be different in the aspects of both parameters and dimensions, and the leader can have unknown control input. A TVOF tracking protocol and a design algorithm are presented using the neighboring interaction. In the proposed protocol, a distributed observer with adaptive updating mechanism is constructed for each follower to asymptotically estimate the state of the leader under the influences of the leader's unknown input firstly. Then, a local formation controller is presented by utilizing the distributed observer, the local state observer and the desired formation vector. Based on the Lyapunov stability theory, it is proved that the expected TVOF tracking can be accomplished by the heterogeneous multi-agent systems in the presence of the leader's unknown input. Furthermore, a continuous TVOF tracking protocol with σ-modification adaptive law is proposed to avoid the large chattering phenomenon.

This paper investigates the time-varying formation robust tracking problems for high-order linear multiagent systems with a leader of unknown control input in the presence of heterogeneous parameter uncertainties and external disturbances. The followers need to accomplish an expected time-varying formation in the state space and track the state trajectory produced by the leader simultaneously. First, a time-varying formation robust tracking protocol with a totally distributed form is proposed utilizing the neighborhood state information. With the adaptive updating mechanism, neither any global knowledge about the communication topology nor the upper bounds of the parameter uncertainties, external disturbances and leader’s unknown input are required in the proposed protocol. Then, in order to determine the control parameters, an algorithm with four steps is presented, where feasible conditions for the followers to accomplish the expected time-varying formation tracking are provided. Furthermore, based on the Lyapunov-like analysis theory, it is proved that the formation tracking error can converge to zero asymptotically. Finally, the effectiveness of the theoretical results is verified by simulation examples.

Nash equilibrium seeking problems for $N$ -coalition noncooperative games are studied in this paper, where the players in the game possess second-order fully-actuated dynamics with disturbances and uncertainties. The players in one coalition focus on the minimization of the coalition cost instead of individual costs. Moreover, only measurements of the cost functions can be accessed in consideration that their explicit expressions cannot be available in complex application environments. An extremum seeking-based approach is proposed to estimate the gradients of the cost functions that are obtained by dynamic average consensus protocols. Sinusoid signals, required to have different frequencies, are used as perturbations in the strategy while the dynamic disturbances and uncertainties are compensated by introducing an extended state observer. Convergence results are proved via averaging and singular perturbation analysis. Then confrontation of two unmanned aerial vehicle (UAV) swarms in territory-defense scenario is introduced and tasks for UAVs are designed. Countermeasures for the UAVs are obtained by utilizing the Nash equilibrium seeking strategy in the two-coalition noncooperative game. Numerical examples are provided and the effectiveness of the proposed strategy is verified.