Basis-function optimization for subspace-based nonlinear identification of systems with measured-input nonlinearities

For nonlinear systems with measured-input non-linearities, a subspace identification algorithm is used to identify the linear dynamics with the nonlinear mappings represented as a linear combination of basis functions. A selective-refinement technique and a quasi-Newton optimization algorithm are used to iteratively improve the representation of the system nonlinearity. For both methods, polynomials, splines, sigmoids, wavelets, sines and cosines, or radial basis functions can be used as basis functions. Both approaches can be used to identify nonlinear maps with multiple arguments and with multiple outputs.