An analytical adaptive optimal control approach without solving HJB equation for nonlinear systems with input constraints
Bibliographic record
Abstract
Abstract This paper presents an analytical method to solve the optimal control problem for affine nonlinear systems with unknown drift dynamics. A new non‐quadratic cost function over an infinite horizon is presented that considers input constraints and includes the cost of the feed‐forward component of the control law. The mean value theorem for vector‐valued functions has been used to derive an integral form of this theorem. Based on this theorem, a rigorous proof is provided demonstrating that the cost function can be converted into another form. In the presence of input constraints, this converted form enables extracting the optimal control solution without solving the HJB equation. Additionally, unknown nonlinearity effects in drift dynamics are compensated in the control input. This is accomplished by estimating the unknown drift dynamics via an adaptive neural network (NN) approach. It is proven that the states and weights of NN are uniformly ultimately bounded based on a Lyapunov technique. The necessary and sufficient conditions are provided that ensure the optimality of the infinite horizon optimal control problem with a discount factor. As a result, it is demonstrated that the proposed approach satisfies the optimality criteria. To evaluate the effectiveness of the proposed approach, simulation examples are provided.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 source (direct Gemma or distilled Codex), 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".