Parameter Identification For A Class Of Nonlinear Systems

Nonlinear systems widely exist in practical applications, like communication systems,chemical processes, biomedical systems and so on. Therefore, nonlinear systems identifica-tion is quite significant both in theory and application. This thesis presents the identificationalgorithms for a class of nonlinear systems based on the National Natural Science Foundationof China. By employing the multiinnovation principle, the auxiliary model identification, theiterative identification principle, the gradient search principle and the Newton method, theidentification of nonlinear systems are studied, the innovation research results are as follows:1. The identification problem of FIR systems with input nonlinearity is investigated. Bymeans of the gradient search principle and the multiinnovation principle, the projectionalgorithm, the stochastic gradient algorithm and the multiinnovation stochastic gradientalgorithm are derived, where the combined parameters in the system model are identifiedseparately. Further, the simulations are carried out for comparison and analysis.2. In order to reduce the sensitivity of the projection algorithm to noise, and to improve theconvergence rate of the stochastic gradient algorithm, a Newton recursive identificationalgorithm and a Newton iterative identification algorithm are derived by using the Newtonmethod. The simulation results show that the Newton iterative algorithm performs muchbetter for nonlinear systems with noise than the other algorithms.3. Considering the identification of the input nonlinear systems with the colored noise, anextended projection algorithm, a simplified extended projection algorithm, and an extendedstochastic gradient algorithm by gradient search principle are derived to identify systemparameter with the residuals instead of the unpredictable noises. Since the projectionalgorithm is very sensitive to the noise and the extended stochastic gradient algorithmhas slow convergence rate and undesirable estimation accuracy, by introducing a forgettingfactor to the extended stochastic gradient algorithm, the convergence rate of the algorithmis faster. An extended Newton recursive algorithm and an extended Newton interactivealgorithm are derived for comparison. In the simulation, the results show that the Newtoniterative algorithm can get better accurate parameter estimates.4. According to the gradient search principle, the auxiliary model identification, the Newtonmethod and iterative identification, the auxiliary model projection, the auxiliary modelstochastic gradient, the auxiliary model Newton recursive and the auxiliary model Newton iterative identification algorithms are derived for input nonlinear output error type systems.The simulation examples test the proposed algorithms and compare with each other. Theresults show that the auxiliary model Newton iterative identification algorithm works quitewell.The main constructive algorithms and results of the dissertation are concluded, and theidentification di?culties for nonlinear systems and further research topics in this area are dis-cussed.