量化自适应控制下多层复杂网络的固定时间同步

Multi-layer complex networks are ubiquitous in natural and engineered systems, yet achieving rapid and predictable synchronization in such networks remains challenging due to nonlinear dynamics, parameter uncertainties, and practical constraints such as limited communication bandwidth. This paper investigates the fixed-time synchronization problem in multi-layer complex networks characterized by nonlinear node dynamics and intra-layer couplings, under the influence of quantized state feedback and adaptive update laws. Within a quantized control framework, we first propose a gain-bounded adaptive quantized control protocol that incorporates an adaptive mechanism to address uncertainties in network parameters while ensuring that all control gains remain uniformly bounded. This design not only enhances robustness but also guarantees practicality in implementation. Subsequently, for both the proposed adaptive protocol and a more general class of quantized control protocols, we derive the sufficient conditions for achieving fixed-time synchronization by integrating Lyapunov stability theory, fixed-time stability criteria, and advanced differential inequality techniques. Explicit and tight upper bounds for the settling time of synchronization are established, offering theoretical guarantees for convergence performance. Finally, extensive numerical simulations on representative multi-layer network topologies are conducted to validate the theoretical findings. The results demonstrate that both control strategies effectively achieve fixed-time synchronization with accurate time estimates, highlighting the advantages of the proposed method in balancing control effort, convergence speed, and robustness against quantization errors. In addition, these contributions can provide a solid theoretical foundation and practical guidelines for the design and analysis of synchronization protocols in complex networked systems with quantized information and parametric uncertainties.