Extension of local linear controllers to global piecewise affine controllers for uncertain non-linear systems
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Bibliographic record
Abstract
A two-step controller synthesis method is proposed in this article for a class of uncertain non-linear systems described by piecewise affine differential inclusions. In the first step, a robust linear controller is designed for the linear differential inclusion that describes the dynamics of the non-linear system close to the equilibrium point. In the second step, a stabilising piecewise affine controller is designed that coincides with the linear controller in a region around the equilibrium point. The proposed method has two objectives: global stability and local performance. It thus enables us to use well-known techniques in linear control design for local stability and performance while delivering a global piecewise affine controller that is guaranteed to stabilise the non-linear system. To construct the required theoretical framework, a stability theorem for non-smooth Lyapunov functions is presented and proved. The new method will be applied to two examples.
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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 | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| 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