# Correct-by-Design Control of Parametric Stochastic Systems

arXiv: https://arxiv.org/abs/2210.08269 · HTML: https://mlsanity.com/paper/2210.08269/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Oct 2022.

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

- [Average Reward Reinforcement Learning for Omega-Regular and Mean-Payoff Objectives](https://mlsanity.com/paper/2505.15693/) (2025)

## Abstract (arXiv)

This paper addresses the problem of computing controllers that are correct by design for safety-critical systems and can provably satisfy (complex) functional requirements. We develop new methods for models of systems subject to both stochastic and parametric uncertainties. We provide for the first time novel simulation relations for enabling correct-by-design control refinement, that are founded on coupling uncertainties of stochastic systems via sub-probability measures. Such new relations are essential for constructing abstract models that are related to not only one model but to a set of parameterized models. We provide theoretical results for establishing this new class of relations and the associated closeness guarantees for both linear and nonlinear parametric systems with additive Gaussian uncertainty. The results are demonstrated on a linear model and the nonlinear model of the Van der Pol Oscillator.