Weighted least squares based recursive parametric identification for the submodels of a PWARX system

A piecewise affine autoregressive system with exogenous inputs (PWARX) is composed of a finite number of ARX subsystems, each of which corresponds to a polyhedral partition of the regression space. In this work a weighted least squares (WLS) estimator is suggested to recursively estimate the parameters of the ARX submodels, in which a sequence of kernel functions are introduced. Conditions on the input signal and the PWARX system are imposed to guarantee the almost sure convergence of the WLS estimates. Some numerical examples are included to illustrate performances of the algorithm.