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.

Time-varying formation tracking (TVFT) control problems for a team of unmanned aerial vehicles (UAVs) with switching and directed interaction topologies are investigated, where the follower UAVs realize a given time-varying formation while tracking the leader UAV. A TVFT control protocol is firstly constructed utilizing local neighboring information, where the information of the leader UAV is only available to partial followers and the neighborhood can be switching. An algorithm composed of four steps is provided to design the TVFT protocol. It is proved that the UAV swarm system can realize the TVFT using the designed protocol if the dwell time for the switching directed topologies is larger than a fixed threshold and the TVFT feasibility condition is satisfied. Based on the ultrawideband positioning technology, a quadrotor UAV formation control platform with four quadrotor UAVs is given. The obtained theoretical results are applied to solve the target enclosing problems of the UAV swarm systems. A flying experiment for three follower quadrotor UAVs to enclose a leader quadrotor UAV is carried out to verify the effectiveness of the presented results.

The adaptive practical optimal time-varying formation tracking problems of the disturbed high-order multi-agent systems with a noncooperative leader are considered. Different from the former achievements, the effects of the leader’s unknown control input and followers’ external disturbances are both considered in the optimal time-varying formation tracking issues. Firstly, an adaptive practical optimal time-varying formation tracking protocol is proposed. The extended state observers and adaptive neural networks are introduced to estimate the integrated uncertainty and value function for the adaptive protocol, respectively. Then, an algorithm is presented to determine the control parameters for the adaptive optimal protocol and neural networks weights update laws. Thirdly, the stability and the optimal formation tracking property are analyzed for the closed loop disturbed high-order multi-agent system. Finally, the numerical simulation results are presented for revealing the effectiveness of the obtained theoretical methods.

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.

Time-varying group formation-containment tracking problems for general linear multiagent systems with unknown control input are investigated. Agents are classified into tracking leaders, formation leaders, and followers and assigned in groups. Tracking leaders with unknown control inputs provide unpredictable trajectories as macroscopic moving references. Formation leaders accomplish desired subformations while following the trails of tracking leaders. At the same time, followers converge into different convex hulls spanned by formation leaders. First, formation-containment tracking protocols are designed with neighboring relative information and effects of unknown input of tracking leaders. Then, the design of group division is analyzed by adjusting the properties in Laplacian matrices, which represent interaction relationships. An algorithm to determine the parameters in control protocols is proposed, and the formation tracking feasible constraint is presented. Next, it is proved that the general linear multiagent system can achieve time-varying group formation-containment control effectively with errors uniformly asymptotically converging to zero under designed protocols. Finally, a numerical simulation is given to verify the effectiveness of obtained theoretical results.