Identification of the nonlinear systems based on the kernel functions

Abstract

Constructing an appropriate membership function is significant in fuzzy logic control. Based on the multi‐model control theory, this article constructs a novel kernel function which can implement the fuzzification and defuzzification processes and reflect the dynamic quality of the nonlinear systems accurately. Then we focus on the identification problems of the nonlinear systems based on the kernel functions. Applying the hierarchical identification principle, we present the hierarchical stochastic gradient algorithm for the nonlinear systems. Meanwhile, the one‐dimensional search methods are proposed to solve the problem of determining the optimal step sizes. In order to improve the parameter estimation accuracy, we propose the hierarchical multi‐innovation forgetting factor stochastic gradient algorithm by introducing the forgetting factor and using the multi‐innovation identification theory. The simulation example is provided to test the proposed algorithms from the aspects of parameter estimation accuracy and prediction performance.

Noniterative tensor network‐based algorithm for Volterra system identification

“…System identification can serve as a powerful tool to generate a data‐driven dynamic model to capture the major dynamics between the input/output signals when first principles modeling is difficult or even intractable for complex physical systems. This tool is widely used in signal processing applications including filtering, state estimation, prediction, or feedback controller design 1‐5 . Linear time‐invariant model has been intensively studied and well used in many applications over the last few decades due to its simplicity and a systematic group of techniques based on it 1,6‐11 .…”

“…This tool is widely used in signal processing applications including filtering, state estimation, prediction, or feedback controller design. [1][2][3][4][5] Linear time-invariant model has been intensively studied and well used in many applications over the last few decades due to its simplicity and a systematic group of techniques based on it. 1,[6][7][8][9][10][11] In case the relationship between input/output data exhibits nonlinear phenomena, a nonlinear model approximation is needed.…”

The Elastic Net Regularized Extreme Learning Machine for State of Charge Estimation

“…The burgeoning progress in novel energy vehicles, particularly electric vehicles, has been significantly propelled by the concurrent challenges of the global energy crisis and the demand for environmental conservation. [1][2][3][4][5][6] Lithium-ion batteries served as an indispensable component in electric vehicles, have been reported in numerous studies. [7][8][9] The introduction of lithium-ion batteries has led to considerable safety concerns, posing significant risks to individuals and their property.…”

“…Adaptive approaches, such as the Kalman filter (KF) and particle filter (PF), are proposed to estimate the SOC. 5,[20][21][22] The KF requires an equivalent circuit model, which is typically a state space model, where the SOC is usually considered as a state variable. The extended Kalman filter (EKF) is used to estimate the SOC due to the battery's nonlinear behavior.…”

The Bidirectional Gate Recurrent Unit Based Attention Mechanism Network for State of Charge Estimation

“…29 Adaptive approach.-The adaptive approaches include the kalman filter (KF), particle filter (PF) and etc. 9,[30][31][32] KF is a method of recursive linear minimum variance estimation. The minimum variance estimation is constructed through the observed real-time state vector and the state vector at the previous instant.…”