Adaptive noise control for almost sure exponential stability of stochastic coupled jump diffusion systems

This paper uses an adaptive noise control strategy to investigate the almost sure exponential stability of a class of stochastic coupled networks influenced by jump diffusion. Due to the strong dependence of the diffusion coefficient on adaptive signals, traditional Lyapunov methods face significant limitations in handling stochastic noise. Different from most existing literature, a novel martingale-based approach that leverages the positive effects of control-dependent stochastic noise is presented to maintain system stability. Besides, the adaptive noise control mechanism adjusts dynamically based on the system state, enhancing the stability of the system against unpredictable jumps. Finally, an example of single-link arms is provided to argue the feasibility and efficacy of the proposed control strategy.