Identification of decoupled polynomial narx model using simulation error minimization

The Polynomial Nonlinear Auto-Regressive eXogenous input (P-NARX) model, a multivariable polynomial of past input and output values, is a widely used equation error nonlinear system model. The number of model parameters grows rapidly with the polynomial degree, and with the number of past inputs and outputs, but can be reduced significantly by adopting a decoupled structure, consisting of a transformation matrix followed by a bank of single-input single-output polynomials whose outputs are summed to produce the final output. Prediction Error Minimization (PEM) is a classical approach for the identification of both linear and nonlinear systems. Models trained using PEM may not be suitable for system simulation, where the model only has access to the system's inputs. In this paper, an identification method based on Simulation Error Minimization (SEM) for Decoupled P-NARX models is proposed. The proposed algorithm is applied to data from two nonlinear system identification benchmarks and the performance is compared to a previous PEM based algorithm.