Novel Discretized Zeroing Neural Network Models for Time-Varying Optimization Aided With Predictor-Corrector Methods.
Summary
New predictor-corrector (PC) methods enhance the stability of discrete zeroing neural networks (DZNNs) for time-varying optimization (TVO) problems. These PC-DZNN models improve dynamical stability and efficiently solve complex motion planning tasks.
Area of Science:
- Numerical analysis and computational mathematics.
- Robotics and control systems.
- Optimization theory.
Background:
- Time-varying optimization (TVO) problems are crucial in dynamic systems.
- Discrete zeroing neural networks (DZNNs) are used for TVO, but their stability is limited by stepsize.
- Existing DZNN models, like Zhang et al. discretization (ZD-DZNN), face challenges in dynamical stability due to stepsize constraints.
Purpose of the Study:
- To derive novel predictor-corrector (PC) methods with three-order convergent precision.
- To develop specific general linear three-step (GLTS) rules for enhanced DZNN models.
- To improve the dynamical stability and efficiency of DZNNs for solving discrete TVO problems.
Main Methods:
- Derivation of three-order convergent predictor-corrector (PC) methods.
- Formulation and study of a discrete time-varying optimization (TVO) problem.
- Application of specific GLTS-type PC-DZNN models to solve the TVO problem.
- Theoretical analysis of DZNN stability improvements using PC methods.
Main Results:
- The proposed PC methods achieve three-order convergent precision.
- PC-DZNN models demonstrate enhanced dynamical stability compared to ZD-DZNN.
- Numerical simulations confirm the improved stability of PC-DZNN models.
- Efficient solutions were obtained for motion planning of a PA10 manipulator and UR5 kinematics.
Conclusions:
- Predictor-corrector methods significantly enhance the stability of DZNNs for TVO problems.
- GLTS-type PC-DZNN models offer a robust approach for solving complex dynamic optimization tasks.
- The developed methods provide efficient and stable solutions for real-world robotics applications.
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