Recursive Stability Modeling in Complex Networked Systems with Adaptive Learning Structures

Abstract

Stability in long-term change in changing networked systems with dynamic parameters and recursive feedback loops has remained a challenge. The study presents a new multi-layered recursive stability modelling framework that places adaptive learning blocks and the topology of the system dynamics into consideration. Control architectures that are constrained by decentralization provide balance in lieu of setpoint thresholds that are used to define system behaviour. Studied many different network topologies to demonstrate that, through rigorous constructs in terms of definitions, simulations, and experiments, control in terms of recursive learning improvements limits the convergence time, as well as improves the robustness of the system and stability of the feedback loop, even in the noisy, asynchronous, or resource-limited environment. The data also shows that the system performs well when structural perturbations or information lags are added, but indicates that metasystem reinforcement adaptation improves adaptive performance significantly. These results contribute to basic principles of smart control in networks and offer a flexible basis of robust structural pathways in automation, distributed sensing, and the cyber-physical systems business sector, in which scalable integration can be achieved. The paper ends with a discussion regarding the concept of modular extension in federated learning networks and digital twins.