Fractional-order Iterative Identification Of Nonlinear Equation Error Systems

Nonlinear systems can well describe complex industrial processes,physical processes and natural phenomena,which has been an active research topic for decades.In this paper,the parameter identification problem of fractional-order nonlinear equation error class systems are studied based on iterative search technology,combined with multi-information identification theory and key term separation,and the following research results are obtained:(1)For the finite impulse response autoregression model in the equation error class systems,the pseudo-linear regression model is obtained by introducing the key term separation to parameterize the fractional-order nonlinear finite impulse response system.For the fractional-order nonlinear finite impulse response system,a key term separation auxiliary model gradient-based iterative algorithm and a key term separation auxiliary model multi-innovation gradient-based iterative algorithm are derived on the basis of the auxiliary model idea and the multi-information identification theory.(2)Considering the fractional-order nonlinear closed-loop system under the interference of color noises,the model decomposition technique is used to decompose the complex system into two subsystems that are easy to be identified,and the effective identification of parameters is realized by combining the idea of interaction estimation and multi-information identification theory.A two-stage gradient iterative method for fractional-order nonlinear closed-loop system and a two-stage gradient iterative method for moving data window are derived,and the analysis of the calculation quantity is also given.(3)For the fractional-order nonlinear block structure system disturbed by color noise,the interaction estimation theory and all known data information are used to estimate the interaction of parameters among subsystems in order to solve the influence of unmeasured noise items on the information vector by combining the idea of normalization hypothesis and the principle of hierarchical identification.A two-stage(hierarchical)over-parameterized gradient iterative algorithm and a two-stage(hierarchical)gradient iterative algorithm for key term separation are derived for fractional-order nonlinear block structures.In this paper,several parameter estimation algorithms of fractional-order nonlinear equation error systems are derived,the calculation steps of the algorithms are summarized,and numerical simulation is carried out to verify the effectiveness of the algorithm.