Adaptive Tube-Based Model Predictive Control with a Control Barrier Function-Based Safety Layer
Bibliographic record
Abstract
Ensuring safety in safety-critical and autonomous systems requires control frameworks that balance performance with strict constraint satisfaction. Model Predictive Control (MPC) naturally handles constrained optimization but standard robust MPC is often overly conservative under fixed uncertainty bounds. Learning-Based MPC (LB-MPC) leverages learned dynamics models to reduce model mismatch and enhance performance, yet its safety guarantees are still limited. Concurrently, Control Barrier Functions (CBFs) have become a prominent method for enforcing forward invariance of safe sets, though their combination with MPC can create tensions between nominal performance and safety constraints. This paper introduces a two-layer safe learning-based control framework that: (i) adapts robustness online via a Certainty-Adaptive Tube LB-MPC, and (ii) guarantees safety through a CBF-Aware Safety Layer that integrates cost shaping with quadratic program (QP) filtering. Under mild assumptions, recursive feasibility and forward invariance are established, and the method is validated on benchmark problems, including a one-dimensional integrator and an inverted pendulum.. The results demonstrate enhanced safety and reduced conservatism relative to fixed-tube LB-MPC and standalone CBFbased safety filters.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 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".