Milne-Hamming Method With Zeroing Neural Network for Time-Varying Nonlinear Optimization and Redundant Manipulator
Summary
A new Milne-Hamming discrete zeroing neural network (DZNN) model improves time-varying nonlinear optimization. This method offers enhanced stability and accuracy over existing DZNN models for complex problems.
Area of Science:
- Computational mathematics
- Neural network optimization
- Applied mathematics
Background:
- Continuous and discrete zeroing neural networks (ZNN) are established for optimization.
- Existing discrete ZNN (DZNN) models have limitations in stability and accuracy for complex problems.
Purpose of the Study:
- To propose and analyze a novel Milne-Hamming discrete ZNN (MHDZNN) model.
- To address time-varying nonlinear optimization (TV-NO) problems with functional limitations.
Main Methods:
- Discretization of the ZNN model using a four-step Milne-Hamming (MH) method.
- Theoretical analysis of the MHDZNN model for absolute stability and error convergence.
- Numerical simulations and application to redundant manipulators.
Main Results:
- The MHDZNN model demonstrates an extended absolute stability domain of $\mu \in (0,1/2)$.
- Achieves a convergent error of order $O(\tau ^{5})$ with a truncation error constant of $1/40$.
- Outperforms existing explicit DZNN models in terms of convergent error and stability domain.
Conclusions:
- The proposed MHDZNN model offers superior accuracy and stability for TV-NO problems.
- The MH method effectively discretizes ZNN for enhanced performance.
- Validated effectiveness through numerical simulations and a practical application.
Related Concept Videos
01:21Linear Approximation in Time Domain
58
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
58
01:29Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
34
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
34
01:25Multimachine Stability
115
Multimachine stability analysis is crucial for understanding the dynamics and stability of power systems with multiple synchronous machines. The objective is to solve the swing equations for a network of M machines connected to an N-bus power system.
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:
115