A Hybrid-Gain ZNN With Precisely Predefined-Time Convergence for Time-Variant LMVI and Its Applications to UR Robotic...

Area of Science:

• Computational neuroscience
• Artificial intelligence
• Applied mathematics

Background:

• Time-variant-gain zeroing neural networks (TVG-ZNNs) are effective for time-variant linear matrix-vector inequalities (TVLMVIs).
• Existing TVG-ZNNs with nonlinear activations have high computational costs and imprecise convergence time, while linear activation variants lack finite-time convergence.
• Increasing gain values in conventional TVG-ZNNs escalate computational demands over time.

Purpose of the Study:

• To introduce a novel hybrid-gain ZNN without nonlinear activation (HG-ZNN-WNAF) for solving TVLMVIs.
• To achieve precisely predefined-time convergence and reduce computational costs for TVLMVI solvers.
• To ensure robustness in both noisy and noise-free environments.

Main Methods:

• Design of a novel hybrid gain for a linear activation function-based ZNN (HG-ZNN-WNAF).
• Ensuring the hybrid gain value remains bounded to prevent escalating computational costs.
• Theoretical analysis and validation through simulations and physical experiments.

Main Results:

• The HG-ZNN-WNAF demonstrates precisely predefined-time convergence for TVLMVIs.
• The model achieves reduced computational costs due to its piecewise hybrid gain and linear activation.
• The HG-ZNN-WNAF exhibits superior performance in convergence speed, robustness, and computational efficiency compared to state-of-the-art methods.

Conclusions:

• The proposed HG-ZNN-WNAF effectively addresses the limitations of existing TVG-ZNNs for TVLMVI solutions.
• Precise predefined-time convergence and computational efficiency are key advantages of the novel approach.
• The HG-ZNN-WNAF offers a robust and computationally efficient solution for TVLMVIs in various conditions.