Separable synchronous redundant rule-based multi-innovation predictive gradient algorithms and convergence analysis for nonlinear ExpARX models

This paper studies the parameter identification and time-delay estimation problem for the nonlinear exponential autoregressive with exogenous input (ExpARX) models. To overcome the limitations of the traditional gradient algorithms, which have slow convergence and low identification accuracy, this paper proposes a modified predictive gradient algorithm through using the multi-innovation theory. Due to the extensive number of parameters, the time-delay ExpARX model is segmented into two subsystems by using the hierarchical principle. On the basis of the detached parameters, a modified separable synchronous predictive gradient algorithm is proposed. Moreover, the convergence of the proposed algorithm is proved. Through analyzing the computational efficiency, it has been demonstrated that the decomposition principle reduces computational workload and enhances computational efficiency. Finally, a simulation example and a real-life example of piezoelectric ceramics are used to verify the effectiveness of proposed algorithms.