Leveraging Control Inputs to Enforce Constraints in Differential Dynamic Programming for Nonlinear Optimization*
Bibliographic record
Abstract
Differential Dynamic Programming (DDP) has become a popular strategy for optimizing nonlinear dynamic systems due to its algorithmic efficiency and precision in complex control tasks. The goal to integrate inequality constraints into DDP has sparked considerable interest, aiming to extend its utility to more demanding situations with strict operational constraints. This study provides an extension to the conventional control-limited DDP framework, introducing a methodology that leverages control inputs during the backward pass to incorporate inequality constraints. Our methodology enhances the efficiency of DDP and expedites its convergence in a variety of scenarios. We present our method in two variants: the first handles inequality constraints that are functions of both state and control variables, and the second leverages the concept of relative degree from nonlinear control theory to handle inequality constraints that are solely dependent on state variables. Through simulations on an inverted pendulum and a nonholonomic 2D car, we benchmark our approach against established methods such as Constrained DDP (CDDP) and primal-dual interior-point DDP (IPDDP). The results showcase our method’s superior convergence rate and trajectory efficiency, particularly highlighting the efficacy of employing control inputs for constraint enforcement.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| 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".