Consensus control of fractional-order singular MAS via adaptive pinning under switching topologies

Fractional-order multi-agent systems with singular dynamics and time-varying network structures have gained increasing attention due to their ability to model complex interconnected processes with memory effects and algebraic constraints. In this paper, a novel adaptive pinning control framework for fractional-order singular multi-agent systems under switching topologies is proposed to achieve leader-following consensus. The proposed method simultaneously handles memory-dependent fractional dynamics, algebraic constraints from system singularity, and changing network connectivity, thereby addressing important limitations of traditional methods. By using a distributed adaptive protocol that only needs a small percentage of agents to be pinned, the technique dramatically lowers control complexity without sacrificing performance. Numerical simulations showed the framework’s practical superiority over currently existing methods in terms of convergence rate and robustness, while analytical results based on fractional Lyapunov theory established rigorous stability conditions that account for system uncertainties. Through an integrated approach to managing entangled fractional, singular, and network dynamic characteristics, these contributions enhance the control of intricate multi-agent systems. The proposed framework explicitly handles switching topologies through average dwell-time conditions and jointly connected graphs, providing rigorous stability guarantees under dynamic network changes.