Hierarchical structures in multi-agent systems: Containment control and opinion dynamics

This study extends the Taylor model of opinion dynamics by addressing key limitations and introducing novel elements to enhance its applicability. Specifically, a hierarchy of stubbornness is introduced to represent opinions influenced by prejudices, with agents acting at different levels to shape the behavior of the multi-agent system. Additionally, the impact of time-varying prejudices is analyzed to reflect the dynamic nature of biases in real-world systems. The model is further extended to account for agents with double-integrator dynamics, capturing both position and velocity states. While Taylor's model lacks direct practical correspondence in opinion dynamics for double-integrator systems, its relevance is demonstrated for containment problems in scenarios such as robotic swarms and autonomous vehicles. Numerical simulations validate the effectiveness of the proposed framework in improving control strategies in dynamic and evolving environments.