Low-Gain Stability of Projected Integral Control for Input-Constrained\n Discrete-Time Nonlinear Systems
Bibliographic record
Abstract
We consider the problem of zeroing an error output of a nonlinear\ndiscrete-time system in the presence of constant exogenous disturbances,\nsubject to hard convex constraints on the input signal. The design\nspecification is formulated as a variational inequality, and we adapt a\nforward-backward splitting algorithm to act as an integral controller which\nensures that the input constraints are met at each time step. We establish a\nlow-gain stability result for the closed-loop system when the plant is\nexponentially stable, generalizing previously known results for integral\ncontrol of discrete-time systems. Specifically, it is shown that if the\ncomposition of the plant equilibrium input-output map and the integral feedback\ngain is strongly monotone, then the closed-loop system is exponentially stable\nfor all sufficiently small integral gains. The method is illustrated via\napplication to a four-tank process.\n
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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) | 0.001 | 0.002 |
| Meta-epidemiology (broad) | 0.003 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| 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".