Accelerated Adaptive Gradient Neural Dynamics Models for Solving Time-Variant Lyapunov Equation and Their Applications
The time-variant Lyapunov equation (TVLE) has played an important role in many fields due to its ubiquity and many neural dynamics models have been developed to obtain the online solution of the TVLE. In prevalent methods, the gradient neural dynamics (GND) models suffer from the large residual erro...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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IEEE
2023-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/10078873/ |
| _version_ | 1797858247231668224 |
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| author | Qinrou Li Yuyuan Zhuang Lilan Zou Guancheng Wang |
| author_facet | Qinrou Li Yuyuan Zhuang Lilan Zou Guancheng Wang |
| author_sort | Qinrou Li |
| collection | DOAJ |
| description | The time-variant Lyapunov equation (TVLE) has played an important role in many fields due to its ubiquity and many neural dynamics models have been developed to obtain the online solution of the TVLE. In prevalent methods, the gradient neural dynamics (GND) models suffer from the large residual error due to the lack of predictive computing, while the zero neural dynamics (ZND) models have large computing complexity because of the inverse of the mass matrix in models. To mitigate these deficiencies, an adaptive parameter containing the time-derivative of time-variant parameters in the TVLE is added to the GND model to form the adaptive GND (AGND) model, which enables the AGND model predictive computing as ZND models and inherits the free of matrix inverse from the GND models. Moreover, two strategies are proposed to design the accelerated AGND (AAGND) models that enjoy a faster convergence rate. The accuracy and the convergence rate of AAGND models are theoretically analyzed, indicating that AAGND models achieve zero residual error and a faster convergence rate. In addition, numerical simulations and two applications are provided to verify the theoretical analyses and the efficiency of AAGND models. The experimental results demonstrate that the AAGND model can solve the TVLE with high accuracy and have great potentialities in applications. |
| first_indexed | 2024-04-09T21:10:18Z |
| format | Article |
| id | doaj.art-dfcfe59d4e8448f5966bba6c8f9b5343 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-04-09T21:10:18Z |
| publishDate | 2023-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-dfcfe59d4e8448f5966bba6c8f9b53432023-03-28T23:00:14ZengIEEEIEEE Access2169-35362023-01-0111294742948210.1109/ACCESS.2023.326124610078873Accelerated Adaptive Gradient Neural Dynamics Models for Solving Time-Variant Lyapunov Equation and Their ApplicationsQinrou Li0Yuyuan Zhuang1Lilan Zou2Guancheng Wang3https://orcid.org/0000-0002-6391-6257College of Electronic and Information Engineering, Guangdong Ocean University, Zhanjiang, ChinaCollege of Mathematics and Computer Science, Guangdong Ocean University, Zhanjiang, ChinaCollege of Electronic and Information Engineering, Guangdong Ocean University, Zhanjiang, ChinaCollege of Electronic and Information Engineering, Guangdong Ocean University, Zhanjiang, ChinaThe time-variant Lyapunov equation (TVLE) has played an important role in many fields due to its ubiquity and many neural dynamics models have been developed to obtain the online solution of the TVLE. In prevalent methods, the gradient neural dynamics (GND) models suffer from the large residual error due to the lack of predictive computing, while the zero neural dynamics (ZND) models have large computing complexity because of the inverse of the mass matrix in models. To mitigate these deficiencies, an adaptive parameter containing the time-derivative of time-variant parameters in the TVLE is added to the GND model to form the adaptive GND (AGND) model, which enables the AGND model predictive computing as ZND models and inherits the free of matrix inverse from the GND models. Moreover, two strategies are proposed to design the accelerated AGND (AAGND) models that enjoy a faster convergence rate. The accuracy and the convergence rate of AAGND models are theoretically analyzed, indicating that AAGND models achieve zero residual error and a faster convergence rate. In addition, numerical simulations and two applications are provided to verify the theoretical analyses and the efficiency of AAGND models. The experimental results demonstrate that the AAGND model can solve the TVLE with high accuracy and have great potentialities in applications.https://ieeexplore.ieee.org/document/10078873/Neural dynamicstime-variant Lyapunov equationconvergenceadaptive parameterrobotic control |
| spellingShingle | Qinrou Li Yuyuan Zhuang Lilan Zou Guancheng Wang Accelerated Adaptive Gradient Neural Dynamics Models for Solving Time-Variant Lyapunov Equation and Their Applications IEEE Access Neural dynamics time-variant Lyapunov equation convergence adaptive parameter robotic control |
| title | Accelerated Adaptive Gradient Neural Dynamics Models for Solving Time-Variant Lyapunov Equation and Their Applications |
| title_full | Accelerated Adaptive Gradient Neural Dynamics Models for Solving Time-Variant Lyapunov Equation and Their Applications |
| title_fullStr | Accelerated Adaptive Gradient Neural Dynamics Models for Solving Time-Variant Lyapunov Equation and Their Applications |
| title_full_unstemmed | Accelerated Adaptive Gradient Neural Dynamics Models for Solving Time-Variant Lyapunov Equation and Their Applications |
| title_short | Accelerated Adaptive Gradient Neural Dynamics Models for Solving Time-Variant Lyapunov Equation and Their Applications |
| title_sort | accelerated adaptive gradient neural dynamics models for solving time variant lyapunov equation and their applications |
| topic | Neural dynamics time-variant Lyapunov equation convergence adaptive parameter robotic control |
| url | https://ieeexplore.ieee.org/document/10078873/ |
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