Revealing the true and pseudo-singularly degenerate heteroclinic cycles

This paper studies the parameter estimation problems of feedback nonlinear systems. Combining the multi-innovation identification theory with the negative gradient search, we derive a multi-innovation gradient-based iterative algorithm. In order to reduce the computational burden and further improve the parameter estimation accuracy, a decomposition multi-innovation gradient-based iterative algorithm is proposed by using the decomposition technique. The key is to transform an original system into two subsystems and to estimate the parameters of each subsystem, respectively. A simulation example is provided to demonstrate the effectiveness of the proposed algorithms.

Section: Discussionmentioning

confidence: 99%

Multi‐innovation gradient‐based iterative identification methods for feedback nonlinear systems by using the decomposition technique

Yang

Ding

2023

“…The presented iterative method in this article can combine some mathematical tools [78][79][80][81] and identification techniques [82][83][84][85][86][87][88] to study new parameter estimation algorithm of various dynamic stochastic systems [89][90][91][92][93][94][95] and can be applied to information processing and chemical process control. The steps for implementing the AM-LSI algorithm in ( 19)-( 26) are listed in the following.…”

Section: The Am-lsi Algorithmmentioning

confidence: 99%

Highly‐computational hierarchical iterative identification methods for multiple‐input multiple‐output systems by using the auxiliary models

Xing

Ding

Pan

2023

The identification of multiple‐input multiple‐output (MIMO) systems is an important part of designing complex control systems. This article studies an auxiliary model least squares iterative (AM‐LSI) algorithm for MIMO systems. With the expansion of the system scale and limitations of the computer resources, there is an urgent need for an identification algorithm that provides higher computational efficiency. To address this issue, this article further derives a hierarchical identification model and proposes a new auxiliary model hierarchical least squares iterative (AM‐HLSI) algorithm for MIMO systems by applying the hierarchical identification principle. Through the analysis of the computational efficiency, the AM‐HLSI algorithm has higher computational efficiency than the AM‐LSI algorithm. Additionally, the feasibility of the AM‐LSI and AM‐HLSI algorithms is validated by a simulation example.

“…The proposed algorithm in this article can combine some mathematical tools [77][78][79][80] to study the parameter estimation algorithms of various stochastic systems with disturbances [81][82][83][84][85][86][87] and can be applied to other literatures [88][89][90][91][92][93][94] such as Algorithm 1. The weighted gradient descent algorithm 1: Initial 2: Choose k max and initialize: For k ⩽ 0, ζ(k).…”

Section: 𝜕𝛼mentioning

confidence: 99%

Parameter and order estimation algorithms and convergence analysis for lithium‐ion batteries

Hu,

Liu,

2023

The fractional‐order equivalent circuit model can reflect the internal reaction mechanism of a lithium‐ion battery well. This article aims to design an effective model and optimization method to describe and analyze the operating characteristics of the lithium‐ion battery based on online measurement data. The fractional‐order controlled autoregressive model is derived by exploiting the memory superiorities of the fractional‐order, which comprises the electrochemical impedance spectroscopy and the ‐RC equivalent circuit model as the special cases. The utilization of polynomial properties reduces the difficulty of identification while preserving the ability of the controlled autoregressive model to fit the characteristics of the battery. To realize simultaneous parameter and the order estimation, a weighted gradient descent algorithm is proposed. The approach designs a new gradient direction and fully utilizes the data from the lithium‐ion battery by adding a suitable weighted factor. In addition, the forgetting factor is introduced to speed up convergence and produce more accurate parameter estimation. Furthermore, in order to analyze the convergence of the proposed algorithms, the convergence properties are proved by using martingale convergence theory and stochastic principle. Finally, the experimental simulation result shows the performance of the proposed algorithms.