<p>Active Noise Control (ANC) systems based on Chebyshev nonlinear (CNL) filter suffer from performance degradation in the presence of complex nonlinearities (e.g., nonlinearities with memory). This may be because the Chebyshev nonlinear filter is merely a straightforward expansion of the input samples via power polynomial functions. To overcome this limitation, we propose a novel nonlinear controller for the ANC system based on the generalized Chebyshev nonlinear filter with a convex combination learning mechanism. By leveraging the product of the input sample and higher-order basis functions (with different time shifts), new orthogonal basis functions, including cross-terms, are generated for the generalized Chebyshev nonlinear filter. The convex combination learning mechanism is designed between the Chebyshev polynomial expansion and cross-term expansion blocks, enabling the proposed filter to optimize the contribution of these expanded functions based on nonlinear characteristics, thereby significantly improving system performance. Furthermore, to reduce the computational burden, a data-dependent filtered-x LMS algorithm has been derived to partially update the adaptive filter weights of the cross-terms expansion. Through simulations and computational analysis in diverse nonlinear environments, the proposed ANC system has proven its effectiveness, outperforming conventional ANC systems of equivalent computational complexity.</p>