Imposing steady-state performance on identified nonlinear polynomial models by means of constrained parameter estimation

The authors present a procedure that permits the use of steady-state information to constrain the identification of nonlinear polynomial models. Such a procedure has three main steps. First, a general framework is provided that relates the static function of nonlinear global polynomial models to their terms and parameters. Second, using standard nonlinear programming techniques, a rational function is fitted to the system static function, which is assumed to be known and is used as auxiliary information. Finally, the information gathered in the first two steps is used to write a set of equality constraints that are exactly satisfied by a standard constrained least-squares algorithm used to estimate the parameters of the identified model. It is shown that the resulting model will always have the specified static nonlinearity and will use additional degrees of freedom to fit the dynamics underlying the observed data.