Extended Kalman Filter-Based Observer Design for Semilinear Infinite-Dimensional Systems
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Bibliographic record
Abstract
In many physical applications, the system's state varies with spatial variables as well as time. The state of such systems is modelled by partial differential equations and evolves on an infinite-dimensional space. Systems modelled by delay-differential equations are also infinite-dimensional systems. The full state of these systems cannot be measured. Observer design is an important tool for estimating the state from available measurements. For linear systems, both finite- and infinite-dimensional, the Kalman filter provides an estimate with minimum-variance on the error, if certain assumptions on the noise are satisfied. The extended Kalman filter (EKF) is one type of extension to nonlinear finite-dimensional systems. In this paper we provide an extension of the EKF to semilinear infinite-dimensional systems. Under mild assumptions we prove the well-posedness of equations defining the EKF. Local exponential stability of the error dynamics is shown. Only detectability is assumed, not observability, so this result is new even for finite-dimensional systems. The results are illustrated with implementation of finite-dimensional approximations of the infinite-dimensional EKF on an example.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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