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Explicit Linear Left-and-Right 5-Step Formulas With Zeroing Neural Network for Time-Varying Applications.
IEEE Transactions on Cybernetics
|August 31, 2021
Summary
New explicit linear left-and-right 5-step (ELLR5S) formulas offer sixth-order precision for solving complex systems. These advanced formulas and discrete zeroing neural network (DZNN) models demonstrate superior performance in practical applications.
Area of Science:
- Numerical analysis
- Computational mathematics
- Control theory
Background:
- Conventional time-discretization methods can limit precision and convergence.
- Need for higher-order numerical methods in solving dynamic systems.
Purpose of the Study:
- To propose novel explicit linear left-and-right 5-step (ELLR5S) formulas with sixth-order precision.
- To develop discrete zeroing neural network (DZNN) models using these formulas for dynamic systems.
- To validate the efficacy and superiority of the proposed methods through theoretical analysis and experiments.
Main Methods:
- Development of a general sixth-order ELLR5S formula with four variable parameters.
- Derivation of constraints for zero stability, consistency, and convergence.
- Generation of eight specific sixth-order ELLR5S formulas by parameter selection.
- Application of ELLR5S formulas to design discrete zeroing neural network (DZNN) models.
- Comparison with three conventional discretization formulas.
Main Results:
- Theoretical analyses confirm the performance of ELLR5S formulas and DZNN models.
- Experimental results demonstrate the efficacy and superiority of sixth-order ELLR5S formulas and DZNN models.
- Successful application in angle-of-arrival (AoA) localization and control of redundant manipulators (PUMA560, Kinova).
Conclusions:
- The proposed sixth-order ELLR5S formulas provide a significant advancement over conventional methods.
- The developed DZNN models based on ELLR5S formulas are effective for solving time-varying systems.
- The study substantiates the practical utility and superior performance of the novel numerical approach.
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