Safe-Parking Framework for Fault-Tolerant Control of Transport−Reaction Processes
Bibliographic record
Abstract
This work considers the problem of handling actuator faults in transport−reaction processes described by quasi-linear parabolic partial differential equations (PDEs) subject to input constraints. To this end, first, by exploiting the separation between the fast and slow eigenmodes of the parabolic spatial differential operator in combination with Galerkin’s method, a finite set of ordinary differential equations (ODEs) that captures the dominant dynamics of the PDE system are constructed. This finite ODE system is used to develop a Lyapunov-based model predictive controller which provides an explicit characterization of the set of initial conditions from where closed-loop stability of the parabolic PDE system is guaranteed. This control design is then subsequently used to develop a safe-parking framework for handling faults. In particular, faults which preclude the possibility of maintaining operation at the nominal equilibrium distribution, using the existing robust or reconfiguration-based fault-tolerant control approaches are considered. The key idea is to temporarily maintain the process at an appropriate “safe-park” distribution using the available depleted control action. This “safe-park” distribution is chosen to prevent onset of hazardous situations as well as to ensure smooth resumption of nominal operation upon fault repair. Utilizing the stability region characterization provided by the developed predictive controller, safe-park distributions from the safe-park candidates (equilibrium distributions subject to the remaining functioning and fail-safe values of the failed actuators) are chosen to preserve closed-loop stability upon fault repair. The proposed framework is illustrated on a diffusion−reaction process.
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How this classification was reachedexpand
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 | 0.001 |
| 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 | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.002 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".