# Computing Probabilistic Controlled Invariant Sets

arXiv: https://arxiv.org/abs/1905.04117 · HTML: https://mlsanity.com/paper/1905.04117/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 May 2019.

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

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- [Flipping-based Policy for Chance-Constrained Markov Decision Processes](https://mlsanity.com/paper/2410.06474/) (2024)
- [Probabilistically safe and efficient model-based reinforcement learning](https://mlsanity.com/paper/2504.00626/) (2025)
- [Dyna-Style Safety Augmented Reinforcement Learning: Staying Safe in the Face of Uncertainty](https://mlsanity.com/paper/2604.25508/) (2026)
- [Data-Driven Synthesis of Probabilistic Controlled Invariant Sets for Linear MDPs](https://mlsanity.com/paper/2604.02727/) (2026)
- [Interval POMDP Shielding for Imperfect-Perception Agents](https://mlsanity.com/paper/2604.20728/) (2026)

## Abstract (arXiv)

This paper investigates stochastic invariance for control systems through probabilistic controlled invariant sets (PCISs). As a natural complement to robust controlled invariant sets~(RCISs), we propose finite- and infinite-horizon PCISs, and explore their relation to RICSs. We design iterative algorithms to compute the PCIS within a given set. For systems with discrete spaces, the computations of the finite- and infinite-horizon PCISs at each iteration are based on linear programming and mixed integer linear programming, respectively. The algorithms are computationally tractable and terminate in a finite number of steps. For systems with continuous spaces, we show how to discretize the spaces and prove the convergence of the approximation when computing the finite-horizon PCISs. In addition, it is shown that an infinite-horizon PCIS can be computed by the stochastic backward reachable set from the RCIS contained in it. These PCIS algorithms are applicable to practical control systems. Simulations are given to illustrate the effectiveness of the theoretical results for motion planning.