US Patent 10075201 Adaptive nonlinear system control using robust and low-complexity coefficient estimation

An adaptive controller for a nonlinear system includes a Volterra filter having a transfer function defined by P coefficients. The controller includes an alignment/compensation circuit, which aligns the input samples to the output samples of the nonlinear system. The controller generates a P×P matrix using at least one of input samples to, or output samples from the nonlinear system and normalizes each element of the P×P matrix using a respective normalization factor. The controller generates and solves a system of P linear equations from the P×P matrix and a P×1 matrix derived from input and output samples of the nonlinear system using Cholesky decomposition that may include Fast Inverse Square Root operations and forward backward elimination to generate P values. The controller multiplies each of the P values by an inverse of a respective one of the normalization factors to generate the P coefficients for the Volterra filter.