Identification Of Input Nonlinear Equation-Error Systems With Known Bases

Nonlinear systems widely exist in the industrial production processes and the mathematical models of nonlinear systems are the basis of control. This thesis studies the identification and parameter estimation of the input nonlinear systems with known basis functions. This identification model can better reflect some nonlinear characteristics in practical processes. Therefore, researches on the identification of these systems have the theoretical significance and academic value. The main findings are as follows.(1) For the input nonlinear equation-error system with known basis functions, the overparameterized identification model of the system is derived. A multi-innovation stochastic gradient algorithm is proposed to identify this model based on the multiinnovation identification theory and the gradient search principle, the over-parameterized model produces many unknown parameters and has a high computation load. By decomposing the over-parameterized identification model into several subsystems using the hierarchical identification principle, this paper presents a hierarchical least squares algorithm, analyzes its convergence and compares the identification efficiency with the recursive least squares algorithm.(2) For the input nonlinear equation error system, lots of unknown parameters are produced in the over-parameterizing process, causing the redundant parameters. To overcome this problem, this paper chooses the output of the nonlinear part as the key term and transfers the system into a linear combination of the system outputs,inputs and the key terms. This linear combination model is called the key term separation model and is decomposed into two or three sub-models. Then a multiinnovation stochastic gradient(MISG) algorithm, a two-stage MISG algorithm and a three-stage MISG algorithm are proposed based on the multi-innovation identification theory. The key term separation based recursive least squares(RLS) identification methods are also presented, where the two-stage RLS algorithm and the three-stage RLS algorithm have the lower computational load.(3) For the input nonlinear equation-error system with known bases, the bilinear-parameter system is derived and decomposed into two parameter in linear subsystems based on the bilinear-parameter model decomposition technique. Crossed-estimating the parameters of two subsystems through the stochastic gradient methods, a forgetting factor stochastic gradient algorithm is proposed by introducing a forgetting factor to speed up the gradient search efficiency. A decomposition based recursive least squares algorithm is also proposed. The proposed algorithms avoids the redundant parameter estimation compared with the over-parameterization methods.