# A General Framework for Learning-Based Distributionally Robust MPC of Markov Jump Systems

arXiv: https://arxiv.org/abs/2106.00561 · HTML: https://mlsanity.com/paper/2106.00561/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jun 2021.

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

- [Learning Based NMPC Adaptation for Autonomous Driving using Parallelized Digital Twin](https://mlsanity.com/paper/2402.16645/) (2024)
- [Distributionally Robust Optimization using Cost-Aware Ambiguity Sets](https://mlsanity.com/paper/2303.09408/) (2023)
- [Distributionally Robust Control with End-to-End Statistically Guaranteed Metric Learning](https://mlsanity.com/paper/2510.10214/) (2025)
- [Interactive Trajectory Planning with Learning-based Distributionally Robust Model Predictive Control and Markov Systems](https://mlsanity.com/paper/2605.07768/) (2026)

## Abstract (arXiv)

We present a learning model predictive control (MPC) scheme for chance-constrained Markov jump systems with unknown switching probabilities. Using samples of the underlying Markov chain, ambiguity sets of transition probabilities are estimated which include the true conditional probability distributions with high probability. These sets are updated online and used to formulate a time-varying, risk-averse optimal control problem. We prove recursive feasibility of the resulting MPC scheme and show that the original chance constraints remain satisfied at every time step. Furthermore, we show that under sufficient decrease of the confidence levels, the resulting MPC scheme renders the closed-loop system mean-square stable with respect to the true-but-unknown distributions, while remaining less conservative than a fully robust approach. Finally, we show that the value function of the learning MPC converges from above to its nominal counterpart as the sample size grows to infinity. We illustrate our approach on a numerical example.