This paper considers the distributed affine formation control problem of general linear systems with uncertainty. In affine formation manoeuvre control, the agents are to be capable of producing specified geometric patterns and simultaneously accomplish required manoeuvres, such as scales, translations and rotations. Here, the formation control problem is studied using the stress matrix approach which has similar properties as the Laplacian matrix of a graph, with a major difference being that the edge weights can have positive or negative values. The system stability is analysed using Lyapunov theory. Novel affine formation control laws for general linear systems are presented. Four control laws are presented to address different cases. The proposed laws consider the general linear case, the case with uncertainty and the fully distributed case using robust and adaptive strategies. Under the proposed laws, the collection of agents can track any targets that are affine transforms of a defined reference configuration. Experimental results are presented to demonstrate the effectiveness of the proposed control laws.

考虑具有不确定性的一般线性系统的仿射分布仿射控制问题。在仿射形成操纵控制中，代理应能够产生特定的几何图案并同时完成所需的操纵，例如刻度，平移和旋转。在这里，使用应力矩阵方法研究地层控制问题，该方法具有与图形的拉普拉斯矩阵相似的特性，主要区别在于边缘权重可以具有正值或负值。使用李雅普诺夫理论分析系统的稳定性。提出了适用于一般线性系统的新型仿射形成控制律。提出了四种控制法则以解决不同的情况。拟议法律考虑了一般线性情况，具有不确定性的案例和采用健壮和自适应策略的完全分布式案例。根据提议的法律，代理的集合可以跟踪作为已定义参考配置的仿射变换的任何目标。实验结果表明了所提出的控制律的有效性。