Nonlinear active noise control using Lyapunov theory and RBF network

A new approach to design an efficient algorithm for the ANC system is proposed. The transversal filter-based controllers (FIR and IIR) are first considered. A Lyapunov function of the error is defined and filter coefficients are then adaptively adjusted based on Lyapunov stability theory so that the error converges to zero asymptotically. The design is independent of the statistical properties of signals and its computational complexity is comparable to FXLMS. It has fast error convergence properties and the stability is guaranteed by Lyapunov stability theory. This scheme can be further extended to an efficient nonlinear ANC using an RBF network for excellent performance. Simulation examples are demonstrated to show the degree of noise cancellation this scheme can achieve.