This paper proposes two parameter identification methods for a nonlinear membership function. An equation converted method is introduced to turn the nonlinear function into a concise model. Then a stochastic gradient algorithm and a gradient-based iterative algorithm are provided to estimate the unknown parameters of the nonlinear function. The numerical example shows that the proposed algorithms are effective.

In this study, two modified gradient descent algorithms are proposed for time-delayed models. To estimate the parameters and time-delay simultaneously, a redundant rule method is introduced, which turns the time-delayed model into an augmented model. Then, two GD algorithms can be used to identify the time-delayed model. Compared with the traditional GD algorithms, these two modified GD algorithms have the following advantages: avoid a high-order matrix eigenvalue calculation, thus, are more efficient for large-scale systems; have faster convergence rates, therefore, are (...) more practical in engineering practices. The convergence properties and simulation examples are presented to illustrate the efficiency of the two algorithms. (shrink)

The self-organizing model and expectation-maximization method are two traditional identification methods for switching models. They interactively update the parameters and model identities based on offline algorithms. In this paper, we propose a flexible recursive least squares algorithm which constructs the cost function based on two kinds of errors: the neighboring two-parameter estimation errors and the output estimation errors. Such an algorithm has several advantages over the two traditional identification algorithms: it can estimate the parameters of all the sub-models without prior (...) knowledge of the model identities; has less computational efforts; and can update the parameters with newly arrived data. The convergence properties and simulation examples are provided to illustrate the efficiency of the algorithm. (shrink)