A stepwise simultaneous perturbation stochastic approximation algorithm for stability improvement of active noise control systems

Simultaneous perturbation stochastic approximation (SPSA) has been widely investigated in active noise control (ANC) due to its model-free nature, which eliminates the need for system model estimation. Despite extensive efforts to enhance its performance, SPSA may suffer from instability and convergence issues, particularly in challenging environments. In this paper, we propose a stepwise SPSA algorithm that applies perturbations separately rather than simultaneously, significantly improving stability while maintaining comparable performance to standard SPSA. A Lyapunov-based theoretical analysis proves the algorithm's robust stability. A parameter optimization framework further enhances performance by guiding the selection of perturbation coefficients and step sizes. Numerical simulations and real-time DSP board implementation validate the improved stability and practical effectiveness for ANC applications.