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.

Practical time-varying formation tracking problems for second-order nonlinear multiagent systems with multiple leaders are investigated using adaptive neural networks (NNs), where the time-varying formation tracking error caused by time-varying external disturbances can be arbitrarily small. Different from the previous work, there exists a predefined time-varying formation formed by the states of the followers and the formation tracks the convex combination of the states of the leaders with unknown control inputs. Besides, the dynamics of each agent has both matched/mismatched heterogeneous nonlinearities and disturbances simultaneously. First, a practical time-varying formation tracking protocol using adaptive NNs is proposed, which is constructed using only local neighboring information. The proposed control protocol can process not only the matched/mismatched heterogeneous nonlinearities and disturbances, but also the unknown control inputs of the leaders. Second, an algorithm with three steps is introduced to design the practical formation tracking protocol, where the parameters of the protocol are determined, and the practical time-varying formation tracking feasibility condition is given. Third, the stability of the closed-loop multiagent system is proven by using the Lyapunov theory. Finally, a simulation example is showed to illustrate the effectiveness of the obtained theoretical results.

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.

Robust H∞ guaranteed cost time-varying formation tracking problems for high-order multiagent systems with external disturbances and time-varying delays are considered. It is required that the followers' states need to track the leader's state and to actualize the desired time-varying formation simultaneously. First, this paper devises a linear time-varying formation tracking protocol considering the effects of the delays constituted by the neighboring information. Then, an integral linear quadratic cost function constructed by the control input constraint and the formation tracking error constraint is utilized to analyze the suboptimal robust H∞ guaranteed cost time-varying formation tracking performance. Third, sufficient conditions for actualizing the guaranteed cost time-varying formation tracking with H∞ disturbance attenuation performance are derived, and the conditions for the feasible time-varying formation tracking are raised. To obtain the gain matrix of the protocol, only four linear matrix inequalities are required to be solved. Finally, a numerical simulation example reveals the effectiveness of the acquired results, where five agents achieve the robust H∞ guaranteed cost time-varying formation tracking.

Cooperative guidance issues with impact time consensus against a maneuvering target are considered in this paper. Different from the existing achievements, the expected impact time does not need to be predesigned, which is coordinated by multiple missiles using the neighboring information. First, the impact time consensus command is generated by using the maximum consensus algorithm of time-to-go for each missile. Second, an analytical cooperative guidance law with bias proportional guidance form is proposed for achieving impact time consensus. In addition, the convergence and the stability of the proposed algorithm and guidance law are analyzed. Third, an equivalent guidance experimental platform is constructed for testing the performance of the proposed cooperative guidance strategy. Finally, the numerical simulation and experimental results are presented to verify the effectiveness of the proposed theoretical cooperative guidance methods.