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Cubature-Based Statistical Moment Steering for Nonlinear, Non-Gaussian Trajectory Optimization

  • Daniel C. Qi
  • Kenshiro Oguri
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Abstract

This paper addresses discrete-time non-Gaussian distribution steering in deterministic nonlinear systems. Distribution steering is a problem in which a control policy is designed over a distribution of trajectories rather than optimizing a single trajectory. The challenge with nonlinear systems is that even initially Gaussian distributions evolve into non-Gaussian distributions, often precluding a closed-form representation of the probability density. A method called statistical moment steering applies a cubature-based method to approximate non-Gaussian distributions for an approximate solution to this problem. This paper provides theoretical support and details how it can be solved with sequential convex optimization. A coupled, nonlinear, second-order ordinary differential equation describing a two-dimensional oscillator is provided as a numerical example.

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Cite

BibTeXRIS
BibTeX
@misc{qi2026cubaturebased,
  title = {{Cubature-Based Statistical Moment Steering for Nonlinear, Non-Gaussian Trajectory Optimization}},
  author = {Daniel C. Qi and Kenshiro Oguri},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.33022},
  eprint = {2609.33022},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.33022},
}
RIS
TY  - UNPB
TI  - Cubature-Based Statistical Moment Steering for Nonlinear, Non-Gaussian Trajectory Optimization
AU  - Daniel C. Qi
AU  - Kenshiro Oguri
PY  - 2026
DA  - 2026/09/26
PB  - arXiv
DO  - 10.48550/arxiv.2609.33022
UR  - https://arxiv.org/abs/2609.33022
AB  - This paper addresses discrete-time non-Gaussian distribution steering in deterministic nonlinear systems. Distribution steering is a problem in which a control policy is designed over a distribution of trajectories rather than optimizing a single trajectory. The challenge with nonlinear systems is that even initially Gaussian distributions evolve into non-Gaussian distributions, often precluding a closed-form representation of the probability density. A method called statistical moment steering applies a cubature-based method to approximate non-Gaussian distributions for an approximate solution to this problem. This paper provides theoretical support and details how it can be solved with sequential convex optimization. A coupled, nonlinear, second-order ordinary differential equation describing a two-dimensional oscillator is provided as a numerical example.
ER  -