Identification methods of nonlinear systems based on the kernel functions

Abstract

Membership function identification is the basis for solving the fuzzy control problems. In order to complete the fuzzification process and reflect the dynamic quality of the nonlinear systems accurately, this paper constructs a kernel function-based nonlinear system by introducing the multi-model control strategy, and it has a good performance in fitting nonlinear systems. Then we focus on the parameter estimation problem of the nonlinear systems based on the kernel functions. To overcome the difficulty due to the highly nonlinear relations between the parameters and the model output, we transform the original optimization problem into a quadratic and a nonlinear optimization problems by decomposing the complex identification model into two sub-models. Based on the hierarchical identification principle and the multi-innovation theory, two recursive identification algorithms are proposed for the nonlinear systems. Considering the difficulty to determine the step sizes, we derive the optimal step sizes by the one-dimensional search method. The effectiveness of the proposed algorithms are tested by a numerical example. The simulation results show that the proposed parameter identification methods can identify the nonlinear systems effectively.