A game theory adaptive weighting convex combination FxLMS algorithm for active vibration control

Convex Combination Filtered-x Least Mean Square (C-FxLMS) algorithms face an inherent conflict between achieving rapid convergence speed and smaller steady-state error. To address this limitation, this paper proposes a multi-agent Game Theory Adaptive Weighting (GTAW) based C-FxLMS control strategy for active vibration suppression. The framework integrates two different sub-controllers within a strategic competition process, specifically an efficiency-oriented agent utilizing a variable step size and an accuracy-oriented agent employing a small fixed step size, a state-dependent Nash equilibrium strategy is designed to dynamically modulate the control weights. This strategy allows the system to balance the conflicting objectives of rapid convergence speed and smaller steady-state error. The convergence and stability of the Active Vibration Control (AVC) system are rigorously verified through the construction of a Lyapunov function and boundary analysis. Finally, quantitative results across four distinct scenarios demonstrate that the proposed method achieves an average reduction of 23.9% in steady-state error and a 41.7% decrease in control energy consumption compared to benchmark methods.