Identifying nonlinear systems from experimental data

For a restricted class of nonlinear discrete time systems, two representations, state-space and transfer functions, are considered and methods to move between these are developed. Given a state-space system, closed-form transfer functions via Mathematica programs and nonlinear signal flow graphs are generated and, conversely, a canonical state-space realization is found from the transfer functions. It is supposed that experimental methods provide data over a finite number of frequencies for the first p transfer functions of a nonlinear system. From the second transfer function, the nonlinear system parameters in the beam-square-error match to data are computed by solving systems of algebraic linear equations. For brevity, the discussion is restricted to the case p=2