# Nonlinear Covariance Control via Differential Dynamic Programming

arXiv: https://arxiv.org/abs/1911.09283 · HTML: https://mlsanity.com/paper/1911.09283/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Nov 2019.

## Built on by (most cited first, 6 of 6)

- [Outcome-Driven Reinforcement Learning via Variational Inference](https://mlsanity.com/paper/2104.10190/) (2021)
- [Maximum entropy optimal density control of discrete-time linear systems and Schr"odinger bridges](https://mlsanity.com/paper/2204.05263/) (2022)
- [Advancing Trajectory Optimization with Approximate Inference: Exploration, Covariance Control and Adaptive Risk](https://mlsanity.com/paper/2103.06319/) (2021)
- [Efficient Stochastic Optimal Control through Approximate Bayesian Input Inference](https://mlsanity.com/paper/2105.07693/) (2021)
- [Non-Gaussian Uncertainty Minimization Based Control of Stochastic Nonlinear Robotic Systems](https://mlsanity.com/paper/2303.01628/) (2023)
- [Mutual Information Optimal Density Control of Linear Systems and Generalized Schr"odinger Bridges with Reference Refinement](https://mlsanity.com/paper/2605.09349/) (2026)

## Abstract (arXiv)

We consider covariance control problems for nonlinear stochastic systems. Our objective is to find an optimal control strategy to steer the state from an initial distribution to a terminal one with specified mean and covariance. This problem is considerably more complicated than previous studies on covariance control for linear systems. We leverage a widely used technique - differential dynamic programming - in nonlinear optimal control to achieve our goal. In particular, we adopt the stochastic differential dynamic programming framework to handle the stochastic dynamics. Additionally, to enforce the terminal statistical constraints, we construct a Lagrangian and apply a primal-dual type algorithm. Several examples are presented to demonstrate the effectiveness of our framework.