This paper considers the distributed leader-follower stress-matrix-based affine formation control problem of discrete-time linear multi-agent systems with static and dynamic leaders. In leader-follower multi-agent formation control, the aim is to drive a set of agents comprising leaders and followers to form any desired geometric pattern and simultaneously execute any required manoeuvre by controlling only a few agents denoted as leaders. Existing works in literature are mostly limited to the cases where the agents' inter-agent communications are either in the continuous-time settings or the sampled-data cases where the leaders are constrained to constant (or zero) velocities or accelerations. Here, we relax these constraints and study the discrete-time cases where the leaders can have stationary or time-varying velocities. We propose control laws in the study of different situations and provide some sufficient conditions to guarantee the overall system stability. Simulation study is used to demonstrate the efficacy of our proposed control laws.

翻译：本文研究了具有静态和动态领导者的离散时间线性多智能体系统的分布式领导者-跟随者应力矩阵仿射编队控制问题。在领导者-跟随者多智能体编队控制中，目标是通过仅控制少数被指定为领导者的智能体，驱动包含领导者和跟随者的智能体群体形成任意期望的几何模式，并同时执行所需的机动。现有文献中的研究大多局限于智能体间通信为连续时间设置或采样数据情形，且采样数据情形中领导者被限制为恒定（或零）速度或加速度。本文放宽了这些约束，研究了领导者可具有静止或时变速度的离散时间情形。我们针对不同情形提出了控制律，并给出了保证整个系统稳定性的若干充分条件。仿真研究验证了所提出控制律的有效性。