This paper investigates the finite-horizon ${\mathcal {H}_\infty }$ containment control issue for a general discrete time-varying linear multiagent systems with multileaders. All followers in such a system are driven into a convex hull spanned by multiple leaders, which can be transformed into a problem of tracking a virtual trajectory generated by these leaders. For this purpose, a local state observer is put forward to estimate the state of each agent itself. Then, the estimated state is transmitted to corresponding neighbors governing by an innovation-based event-triggered scheduling protocol. The purpose of the addressed problem is to design both an event-based distributed controller and a state observer such that a prescribed ${\mathcal {H}_\infty }$ containment index can be achieved over a given finite horizon. First, with the help of the completing the square method, a sufficient condition is established to ensure the desired ${\mathcal {H}_\infty }$ containment performance. Then, by resort to a novel nominal energy cost index combined with Moore–Penrose pseudoinverse method, the desired controller and observer parameters are obtained by solving two coupled backward recursive Riccati difference equations. Two positive scalars in proposed nominal energy cost index provide a tradeoff among the controlled tracking errors, the energy of transformed control inputs, and the precision of estimated states. Finally, a simulation example is given to illustrate the usefulness of the proposed theoretical results.

中文翻译：

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事件触发的通信调度下多主体系统的H∞约束控制：有限时限情况

本文研究了有限水平 $ {\数学{H} _ \ infty} $ 具有多引线的一般离散时变线性多主体系统的约束控制问题。这种系统中的所有跟随者都被驱动到由多个领导者跨越的凸包中，这可以转化为跟踪由这些领导者生成的虚拟轨迹的问题。为此，提出了一个本地状态观察器来估计每个代理本身的状态。然后，将估计的状态传输到由基于创新的事件触发的调度协议控制的相应邻居。解决该问题的目的是设计基于事件的分布式控制器和状态观察器，以使 $ {\数学{H} _ \ infty} $ 可以在给定的有限范围内实现围堵指数。首先，借助完成平方法，建立了充分的条件以确保所需的期望值。 $ {\数学{H} _ \ infty} $ 遏制性能。然后，通过使用新颖的名义能源成本指数与Moore-Penrose伪逆方法相结合，通过求解两个耦合的后向递归Riccati差分方程，获得所需的控制器和观测器参数。提议的标称能源成本指数中的两个正标量提供了受控跟踪误差，转换后的控制输入的能量以及估计状态的精度之间的折衷。最后，给出了一个仿真例子来说明所提出的理论结果的有用性。