# Solving Mission-Wide Chance-Constrained Optimal Control Using Dynamic Programming

arXiv: https://arxiv.org/abs/2209.05979 · HTML: https://mlsanity.com/paper/2209.05979/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Sep 2022.

## Built on by (most cited first, 2 of 2)

- [Joint Chance Constrained Safe-Optimal Control](https://mlsanity.com/paper/2606.30829/) (2026)
- [Learning-Based Stochastic Optimal Control with Infinite-Horizon Probabilistic Constraints](https://mlsanity.com/paper/2608.01151/) (2026)

## Abstract (arXiv)

This paper aims to provide a Dynamic Programming (DP) approach to solve the Mission-Wide Chance-Constrained Optimal Control Problems (MWCC-OCP). The mission-wide chance constraint guarantees that the probability that the entire state trajectory lies within a constraint/safe region is higher than a prescribed level, and is different from the stage-wise chance constraints imposed at individual time steps. The control objective is to find an optimal policy sequence that achieves both (i) satisfaction of a mission-wide chance constraint, and (ii) minimization of a cost function. By transforming the stage-wise chance-constrained problem into an unconstrained counterpart via Lagrangian method, standard DP can then be deployed. Yet, for MWCC-OCP, this methods fails to apply, because the mission-wide chance constraint cannot be easily formulated using stage-wise chance constraints due to the time-correlation between the latter (individual states are coupled through the system dynamics). To fill this gap, firstly, we detail the conditions required for a classical DP solution to exist for this type of problem; secondly, we propose a DP solution to the MWCC-OCP through state augmentation by introducing an additional functional state variable.