Hierarchical least squares identification for feedback nonlinear equation-error systems

Because of complex structures, the identification of nonlinear systems is very difficult, especially for closed-loop nonlinear systems (i.e., feedback nonlinear systems). This paper considers the parameter identification of a feedback nonlinear system where the forward channel is a controlled autoregressive model and the feedback channel is a static nonlinear function. Using the hierarchical identification principle decomposes a feedback nonlinear system into two subsystems, one contains the parameters of the linear dynamic block and the other contains the parameters of the nonlinear static block. A hierarchical least squares algorithm and a recursive least squares algorithm are presented for feedback nonlinear systems. The proposed algorithms are simple in principle and easy to implement on-line.