Wenying Mu

This article investigates the parameter identification problem of the stochastic systems described by the multiple‐input controlled autoregressive moving average model. By employing the data filtering technique, the input‐output data is filtered and the original system with colored noise is changed into the system with white noise. Then, based on the hierarchical identification principle, the filtered system is decomposed into two subsystems, one containing the parameters of the linear dynamic block and the other containing the parameters of the nonlinear static block, leading to a filtering‐based hierarchical stochastic gradient algorithm. To enhance the parameter accuracy, a filtering‐based multi‐innovation stochastic gradient algorithm is presented for the multiple‐input nonlinear stochastic systems. Furthermore, the convergence of the filtering‐based hierarchical stochastic gradient algorithm is analyzed, which can guarantee the stability of the algorithm. Finally, a simulation example is provided to verify the effectiveness of the proposed algorithms.

This article presents a decomposition‐based least squares estimation algorithm for the multivariate input nonlinear system. By using the hierarchical identification principle, the algorithm breaks down a nonlinear system into two subsystems, one containing the parameters of the linear dynamic block and the other containing the parameters of the nonlinear static block. Treating the unknown variables contained in the information vector of the model is to replace them with the outputs of an auxiliary model. The comparative results between the hierarchical recursive algorithm developed in this article and the recursive least squares algorithm are provided to test the proposed algorithms have lower computational cost and the higher estimation accuracy. Furthermore, the convergence of the hierarchical recursive algorithm is analyzed, which can guarantee the stability of the algorithm. The simulation results confirm the efficacy of the derived algorithm in effectively estimating the parameters of the nonlinear systems.