Iterative identification methods for multivariable input piecewise nonlinear finite impulse response moving average systems

Multivariable nonlinear systems involve multiple input and output variables, posing challenges in system identification and control design. This paper focuses on the identification issue for multivariable input piecewise nonlinear finite impulse response moving average systems with two-input and single-output, in which the two input nonlinear modules contain dead-zone nonlinearity and variable-gain nonlinearity respectively. By utilizing the switching function and key term separation technique, we derive the system identification model that contains all the linear and nonlinear parameters. Building upon this identification model, we develop an extended gradient iterative algorithm and an extended least squares iterative algorithm by integrating the auxiliary model idea with the iterative identification approach. Furthermore, we provide a comprehensive analysis of the computational efficiency of these two iterative identification algorithms. Finally, we validate the reliability and effectiveness of our proposed algorithms through a simulation example.