Robust ${H}_{{\infty }}$ 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 ${H}_{{\infty }}$ guaranteed cost time-varying formation tracking performance. Third, sufficient conditions for actualizing the guaranteed cost time-varying formation tracking with ${H}_{{\infty }}$ 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 ${H}_{{\infty }}$ guaranteed cost time-varying formation tracking.

中文翻译：

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具有时变延迟的高阶多智能体系统的鲁棒 H∞ 保证成本时变编队跟踪

强壮的 ${H}_{{\infty }}$ 考虑了具有外部干扰和时变延迟的高阶多智能体系统的保证成本时变编队跟踪问题。要求跟随者的状态需要跟踪领导者的状态并同时实现所需的时变编队。首先，本文设计了一种线性时变地层跟踪协议，考虑到由相邻信息构成的延迟的影响。然后，利用由控制输入约束和编队跟踪误差约束构造的积分线性二次代价函数来分析次优鲁棒性 ${H}_{{\infty }}$ 保证成本随时间变化的编队跟踪性能。三、实现保费时变编队跟踪的充分条件 ${H}_{{\infty }}$ 推导了扰动衰减性能，提出了可行的时变编队跟踪条件。为了获得协议的增益矩阵，只需要解决四个线性矩阵不等式。最后，一个数值模拟示例揭示了所获得结果的有效性，其中五个代理实现了鲁棒性 ${H}_{{\infty }}$ 保证成本随时间变化的编队跟踪。