Parameter Identification For Input Nonlinear Systems Based On The Key Term Separation

The input nonlinear system consists of a memoryless nonlinear block followed by a linear dynamical block which can be established by choosing different types of linear and nonlinear blocks to meet requirements of different applications. The block oriented nonlinear system has attracted much attention for its flexible structures and practica-bility. The difficulty of identification is that the input nonlinear system contains the products of the parameters of the nonlinear block and linear block, which leads to the unidentifiability of the parameters. The common solution is the over-parameterization method which introduces a large number of redundant parameters and can not be applied to the identification of multi-variable input nonlinear systems. Under this background,the dissertation "Parameter identification for input nonlinear systems based on the key term separation" aiming at avoiding the redundant parameters to reduce computational burden is meaningful and valuable. The main contributions can be obtained as follows.1. In order to avoid the product terms in identification models of the scalar input nonlin-ear systems, this dissertation uses the key-term separation principle which separates the complex mapping between system inputs and outputs into the directly external mapping and the implicit but exact internal mapping, so that a special form of input nonlinear systems with a minimum number of parameters can be obtained. Fur-ther, the key-term separation principle is extended to the parameter identification of multi-variable input nonlinear systems.2. For the identification problem of input nonlinear systems with unmeasurable terms in the information vector, in the process of implementing the identification algorithms,the true values are replaced by the estimates based on the auxiliary model idea and the algorithms are implemented. Then the parameter estimates can be used to recalculate the unknown terms. In such circulation, satisfied results can be obtained.3. For multi-variable input nonlinear systems, which have complex system structures,a large number of parameters and coupling parameters in each channel of the system,the effectiveness of the recursive algorithms will be compromised. To solve this prob?lem, this dissertation separates the identification model into two or more subsystems and derives the recursive algorithms with the hierarchical principle which realizes the interactive estimation among subsystems.4. Based on the idea above and the least squares principle and the gradient search princi-ple, the least squares iterative algorithms and the gradient based iterative algorithms are studied. Different from the recursive algorithms, the iterative algorithms are cal?culated by using a batch of input and output data which make full use of data and have faster convergence rates and more accurate identification precision.In summary, the effectiveness of the proposed algorithms is illustrated by Matlab simulations. The computational efficiency, the computational steps and the flowcharts of some typical algorithms are discussed.