On Control of a Two-Link Non-Fixed-Base Inverted Pendulum With Guaranteed Uniqueness
Bibliographic record
Abstract
A nonlinear controller with guaranteed uniqueness of Filippov’s solution is presented for controlling a two-link non-fixed-base inverted pendulum. The control system is described by differential equations with discontinuous right-hand sides, which violates the requirements of the conventional solution theories to ordinary differential equations, i.e., the vector fields must be at least Lipschitz continuous. It has been shown that Lyapunov’s second method can be used for such non-smooth systems directly under the condition of existence and uniqueness of Filippov’s solution. For this non-smooth control system with three discontinuity surfaces, the uniqueness of the solution is studied using Filippov’s solution concept. The system itself is a nonlinear, non-autonomous dynamic system without an isolated equilibrium point, which violates the assumption of Lyapunov’s stability theory. To analyze the stability of the control system, a Lyapunov-like function is constructed, which satisfies all the requirements for a Lyapunov function. Such a function can serve as an upper bound of the region in which the pendulum can be stabilized. Simulation results are presented to validate the proposed approach.
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 | 0.000 | 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 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".