This paper studies targeted opinion formation in multi-agent systems evolving over signed, time-varying directed graphs. The dynamics of each agent's state follow a Laplacian-based update rule driven by both cooperative and antagonistic interactions in the presence of exogenous factors. We formulate these exogenous factors as external control inputs and establish a suitable controller design methodology enabling collective opinion to converge to any desired steady-state configuration, superseding the natural emergent clustering or polarization behavior imposed by persistently structurally balanced influential root nodes. Our approach leverages upper Dini derivative analysis and Grönwall-type inequalities to establish exponential convergence for opinion magnitude towards the desired steady state configuration on networks with uniform quasi-strong $δ$-connectivity. Finally, the theoretical results are validated through extensive numerical simulations.

翻译：本文研究了在符号时变有向图上演化的多智能体系统中的目标意见形成问题。在存在外生因素的情况下，每个智能体状态的动态遵循基于拉普拉斯算子的更新规则，该规则由合作性和对抗性相互作用共同驱动。我们将这些外生因素建模为外部控制输入，并建立了一种合适的控制器设计方法，使得集体意见能够收敛到任意期望的稳态配置，从而超越由持续结构平衡的有影响力根节点所强加的自然涌现的聚类或极化行为。我们的方法利用上Dini导数分析和Grönwall型不等式，在具有一致拟强$δ$连通性的网络上建立了意见幅值向期望稳态配置的指数收敛性。最后，通过大量数值模拟验证了理论结果。