Recursive identification of functional-coefficient ARX systems

The recursive identification is considered for functional-coefficient ARX systems, which belong to a certain type of linear parameter-varying (LPV) systems but with parameter-varying mechanism described by nonparametric methods. The geometric ergodicity has been established for FARX systems under rather general conditions with the help of the concept of Q-geometric ergodicity. This implies that the system output is strictly stationary and is β-mixing under an appropriate initial distribution and that its high order moments are finite. By using the recursive estimates of local linear regressions, the nonparametric estimates are derived for nonlinear coefficients and their derivatives. The advantage of the proposed approach is its flexibility to identify high-dimensional complex nonlinear structures without suffering from "curse of dimensionality." The strong consistence has also been established under reasonable conditions. Finally a simulation example is provided to validate the efficacy of the proposed approach.