This article covers the identification of the feedback nonlinear systems. The parameterized nonlinear identification model involves products of system nonlinear part parameters and system linear part parameters. To deal with these product terms, the hierarchical identification based on maximum likelihood is used to decompose the system into two subsystems. The Levenberg–Marquardt and particle swarm optimization methods are applied for identifying the two subsystems, respectively. For the purpose of enhancing the optimization capability of the basic particle swarm optimization method, some improvement strategies are constructed. Thus, the improved particle swarm optimization algorithm which combines the adaptive feedback, the linearly decreasing method and the mutational operator is applied to adaptively adjust the search strategy and improve the ergodicity. The simulation indicates that the derived estimation is effective because it can obtain high identification accuracy and fast convergence speed when identifying the feedback systems. Besides, the case study demonstrates that the proposed method can be well used to identify the electro-hydraulic-servo position system.
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