A Structured Online Learning Approach to Nonlinear Tracking with Unknown Dynamics
Bibliographic record
Abstract
In this paper, an approximate optimal control framework is developed to obtain a tracking controller for a nonlinear system that can be implemented as an online model-based learning approach. Assuming a structured unknown nonlinear system augmented with the dynamics of a commander system, we obtain a control rule minimizing a given quadratic tracking objective function. This is achieved by manipulating the cost and introducing a quadratic value function in terms of some nonlinear bases to comply with the structured dynamics. This problem formulation facilitates the computation of an update rule for the parameterized value function. As a result, a matrix differential equation of the coefficients is extracted, which gives a computationally efficient way for updating the value function and consequently attaining the tracking controller in terms of the reference and state trajectories. The proposed optimal tracking framework can be seen as an online model-based reinforcement learning approach, where we use a system identification method to update the system model, and generate a corresponding control in an iterative way. The presented learning algorithm is validated by implementing tracking control on two nonlinear benchmark problems.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".