Name
Title | ||
|---|---|---|
Neural network-based discrete-time Z-type model of high accuracy in noisy environments for solving dynamic system of linear equations. |
Abstract | ||
|---|---|---|
To solve dynamic system of linear equations with square or rectangular system matrices in real time, a discrete-time Z-type model based on neural network is proposed and investigated. It is developed from and studied with the aid of a unified continuous-time Z-type model. Note that the framework of such a unified continuous-time Z-type model is generic and has a wide range of applications, such as robotic redundancy resolution with quadratic programming formulations. To do so, a one-step-ahead numerical differentiation formula and its optimal sampling-gap rule in noisy environments are presented. We compare the Z-type model extensively with E-type and N-type models. Theoretical results on stability and convergence are provided which show that the maximal steady-state residual errors of the Z-type, E-type and N-type models have orders $$O(tau ^3)$$O(ź3), $$O(tau ^2)$$O(ź2) and $$O(tau )$$O(ź), respectively, where $$tau $$ź is the sampling gap. We also prove that the residual error of any static method that does not exploit the time-derivative information of a time-dependent system of linear equations has order $$O(tau )$$O(ź) when applied to solve discrete real-time dynamic system of linear equations. Finally, several illustrative numerical experiments in noisy environments as well as two application examples to the inverse-kinematics control of redundant manipulators are provided and illustrated. Our analysis substantiates the efficacy of the Z-type model for solving the dynamic system of linear equations in real time. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1007/s00521-016-2640-x | Neural Computing and Applications |
Keywords | Field | DocType |
Recurrent neural network, Discrete-time Z-type model, Dynamic system of linear equations, Noisy environments, Residual error | Convergence (routing),Residual,Mathematical optimization,System of linear equations,Matrix (mathematics),Recurrent neural network,Artificial intelligence,Quadratic programming,Discrete time and continuous time,Artificial neural network,Machine learning,Mathematics | Journal |
Volume | Issue | ISSN |
29 | 11 | 1433-3058 |
Citations | PageRank | References |
9 | 0.46 | 35 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Long Jin | 1 | 86 | 10.66 |
| Yunong Zhang | 2 | 2344 | 162.43 |
| Binbin Qiu | 3 | 35 | 6.70 |