A Hybrid-Gain ZNN With Precisely Predefined-Time Convergence for Time-Variant LMVI and Its Applications to UR Robotic Arm and Multiagent System
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Bibliographic record
Abstract
Time-variant-gain zeroing neural networks (TVG-ZNNs) are among the most powerful solvers for time-variant linear matrix-vector inequalities (TVLMVIs). Although TVG-ZNNs with complex nonlinear activation functions achieve effective convergence within finite or predefined time, they incur high computational costs and face challenges in precisely predefining their actual convergence time. In contrast, TVG-ZNNs with linear activation functions offer lower computational costs but struggle to achieve convergence within a finite or predefined time. In addition, the gain values of most existing TVG-ZNNs tend to increase over time, resulting in a significant rise in computational costs. To address these contradictory issues, we propose a novel hybrid-gain ZNN without a nonlinear activation function (HG-ZNN-WNAF) to solve TVLMVIs in both noisy and noise-free environments. Specifically, a new hybrid gain is cleverly designed to construct the HG-ZNN-WNAF activated by a linear activation function, while ensuring that the gain value does not keep increasing over time. Unlike the state-of-the-art TVG-ZNNs with or without nonlinear activation functions, our proposed HG-ZNN-WNAF achieves precisely predefined-time convergence due to the hybrid gain, meaning its actual convergence time can be accurately predefined. Additionally, the piecewise design of the hybrid gain, along with the use of the simple linear activation function, effectively reduces the model's computational cost. Rigorous theoretical analysis demonstrates the precisely predefined-time convergence ability of the HG-ZNN-WNAF in both noisy and noise-free environments. Simulation and physical experiments validate the theoretical analysis and demonstrate that the HG-ZNN-WNAF achieves state-of-the-art performance in terms of convergence speed, robustness, and computational cost.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it