Gradient Identification Of Nonlinear Equation-Error Closed-Loop Systems

Closed-loop systems and nonlinear characteristics exist commonly in actual industrial processes.At the present,the identification algorithms of linear open-loop systems are mature.How to extend the existing system identification methods to nonlinear closed-loop systems is a hot and difficult topic of identification research.This thesis studies the gradient identification methods for nonlinear closed-loop systems.The main work are listed as follows.1.Closed-loop nonlinear systems always have complex model structures and usually contain product terms of multiple unknown parameters.Existing methods cannot be used directly.Therefore,using the hierarchical identification theory,the nonlinear closed-loop systems can be decomposed into several subsystems,which are identified by the interactive estimation method combined with the negative gradient search principle and the iterative identification idea,respectively.A gradient based iterative algorithm is proposed to realize offline identification of system parameters.2.For nonlinear closed-loop systems,combining with the hierarchical identification principle,a hierarchical stochastic gradient algorithm is proposed.In order to improve the convergence rate and parameter estimation accuracy of the stochastic gradient algorithm,a hierarchical multi-innovation stochastic gradient algorithm is proposed by expanding the length of the innovation with available data.The numerical simulations verify that the multi-innovation technology can improve the accuracy of parameter estimation effectively.3.This thesis develops a generalized hierarchical gradient iterative algorithm for non-linear closed-loop systems with colored noise by using the theory of interactive estimation method.In order to improve the parameter estimation accuracy,applying the data fil-tering technology,with the help of data filtering technology,a filtering based hierarchical gradient iterative algorithm is proposed.Furthermore,combining the data filtering tech-nology with the multi-innovation idea,a filtering based hierarchical stochastic gradient algorithm and a filtering based hierarchical multi-innovation stochastic gradient algorithm are proposed.This thesis gives the procedures and the flowcharts of the hierarchical gradient based iterative algorithm and the hierarchical stochastic gradient algorithm for input nonlinear autoregressive systems and feedback nonlinear autoregressive systems,and gives some numerical simulations to verify the effectiveness of the proposed algorithms.