# Interior Point Differential Dynamic Programming

arXiv: https://arxiv.org/abs/2004.12710 · HTML: https://mlsanity.com/paper/2004.12710/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Apr 2020.

## Built on by (most cited first, 4 of 4)

- [Safe Pontryagin Differentiable Programming](https://mlsanity.com/paper/2105.14937/) (2021)
- [CACTO: Continuous Actor-Critic with Trajectory Optimization -- Towards global optimality](https://mlsanity.com/paper/2211.06625/) (2022)
- [Advances in Trajectory Optimization for Space Vehicle Control](https://mlsanity.com/paper/2108.02335/) (2021)
- [A Differential Dynamic Programming Framework for Inverse Reinforcement Learning](https://mlsanity.com/paper/2407.19902/) (2024)

## Abstract (arXiv)

This paper introduces a novel Differential Dynamic Programming (DDP) algorithm for solving discrete-time finite-horizon optimal control problems with inequality constraints. Two variants, namely Feasible- and Infeasible-IPDDP algorithms, are developed using primal-dual interior-point methodology, and their local quadratic convergence properties are characterised. We show that the stationary points of the algorithms are the perturbed KKT points, and thus can be moved arbitrarily close to a locally optimal solution. Being free from the burden of the active-set methods, it can handle nonlinear state and input inequality constraints without a discernible increase in its computational complexity relative to the unconstrained case. The performance of the proposed algorithms is demonstrated using numerical experiments on three different problems: control-limited inverted pendulum, car-parking, and unicycle motion control and obstacle avoidance.