Adaptive Neural Tracking Control of a Class of Hyperbolic PDE With Uncertain Actuator Dynamics
Bibliographic record
Abstract
This article investigates the adaptive neural tracking control problem for a class of hyperbolic PDE with boundary actuator dynamics described by a set of nonlinear ordinary differential equations (ODEs). Particularly, the control input appears in the ODE subsystem with unknown nonlinearities requiring to be estimated and compensated, which makes the control task rather difficult. It is the first time to consider tracking control of such a class of systems, rendering our contributions essentially different from the existing literature that merely focus on the stabilization problem. By formulating a virtual exosystem to generate a reference trajectory, we propose a novel design of the adaptive geometric controller for the considered system where neural networks (NNs) are employed to approximately estimate nonlinearities, and finite and infinite-dimensional backstepping techniques are leveraged. Moreover, rigorously theoretical proofs based on the Lyapunov theory are provided to analyze the stability of the closed-loop system. Finally, we illustrate the results through two numerical simulations.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| 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 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".