# Chance-Constrained Trajectory Optimization for Non-linear Systems with Unknown Stochastic Dynamics

arXiv: https://arxiv.org/abs/1906.11003 · HTML: https://mlsanity.com/paper/1906.11003/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jun 2019.

## Built on by (most cited first, 1 of 1)

- [Conformal Predictive Programming for Chance Constrained Optimization](https://mlsanity.com/paper/2402.07407/) (2024)

## Abstract (arXiv)

Iterative trajectory optimization techniques for non-linear dynamical systems are among the most powerful and sample-efficient methods of model-based reinforcement learning and approximate optimal control. By leveraging time-variant local linear-quadratic approximations of system dynamics and reward, such methods can find both a target-optimal trajectory and time-variant optimal feedback controllers. However, the local linear-quadratic assumptions are a major source of optimization bias that leads to catastrophic greedy updates, raising the issue of proper regularization. Moreover, the approximate models' disregard for any physical state-action limits of the system causes further aggravation of the problem, as the optimization moves towards unreachable areas of the state-action space. In this paper, we address the issue of constrained systems in the scenario of online-fitted stochastic linear dynamics. We propose modeling state and action physical limits as probabilistic chance constraints linear in both state and action and introduce a new trajectory optimization technique that integrates these probabilistic constraints by optimizing a relaxed quadratic program. Our empirical evaluations show a significant improvement in learning robustness, which enables our approach to perform more effective updates and avoid premature convergence observed in state-of-the-art algorithms.