Optimization-based Control Strategy with Deep Koopman Model for Constrained Complex Nonlinear Systems
Bibliographic record
Abstract
It is well known that a nonlinear system can be represented in a linear lifted feature space according to the Koopman operator theory. However, the approximation errors are always ignored, which may damage the control performance. Therefore, this paper presents a deep Koopman-based two loop control structure, where nonlinearities, uncertainties, and constraints can be handled simultaneously. Namely, a deep Koopman linear model is trained off-line to approximate the dynamic of nonlinear system. Accordingly, an optimization problem is introduced in the outer loop to replan the desired trajectory such that state and input constraints can be satisfied. Considering the model uncertainties introduced by the Koopman linear model, an adaptive robust controller is synthesized in the inner loop to ensure that the optimization result of the outer loop can be strictly tracked. In this way, fast transient response can be reached by the outer loop and the high motion tracking accuracy can be promised by the inner loop. The proposed framework’s advantages and efficacy are evidenced through comparative simulations conducted on a 2-DoF robotic manipulator.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| 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) | 0.001 | 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".