Inexact Primal-Dual Algorithm for DMPC With Coupled Constraints Using Contraction Theory
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Bibliographic record
Abstract
This article studies a distributed model-predictive control (DMPC) strategy for a class of discrete-time linear systems subject to globally coupled constraints. To reduce the computational burden, the constraint tightening technique is adopted for enabling the early termination of the distributed optimization algorithm. Using the Lagrangian method, we convert the constrained optimization problem of the proposed DMPC to an unconstrained saddle-point seeking problem. Due to the presence of the global dual variable in the Lagrangian function, we propose a primal-dual algorithm based on the Laplacian consensus to solve such a problem in a distributed manner by introducing the local estimates of the dual variable. We theoretically show the geometric convergence of the primal-dual gradient optimization algorithm by the contraction theory in the context of discrete-time updating dynamics. The exact convergence rate is obtained, leading the stopping number of iterations to be bounded. The recursive feasibility of the proposed DMPC strategy and the stability of the closed-loop system can be established pursuant to the inexact solution. Numerical simulation demonstrates the performance of the proposed strategy.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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