Data‐driven nonlinear state observation for controlled systems: A kernel method and its analysis
Bibliographic record
Abstract
Abstract This work proposes a data‐driven state observation algorithm for nonlinear dynamical systems, when the true state trajectory is not measurable and hence the states information needs to be reconstructed from input and output measurements. Such a reduction is formed by kernel canonical correlation analysis (KCCA), which (i) implicitly maps the available input–output data into a higher‐dimensional feature space, namely the reproducing kernel Hilbert space (RKHS); (ii) finds a projection of the past input–output data and a projection of the future input–output data with maximal correlation; and (iii) identifies the projected inputs and outputs, namely the canonical variates, as the observed states. We adopt a least squares support vector machine (LS‐SVM) formulation for KCCA, which imposes regularization on the vectors that specify the projections and is amenable to convex optimization. We prove theoretically that, based on the statistical consistency of KCCA, the observed states determined by the proposed state observer has a guaranteed correlativity with the actual states (when properly transformed). Furthermore, such observed states, when supplemented with the information of succeeding inputs, can be used to predict the succeeding outputs with guaranteed upper bound on the prediction error . Case studies are performed on two numerical examples and an exothermic continuously stirred tank reactor (CSTR).
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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 | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| 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".