# A Framework for Adaptive Stabilisation of Nonlinear Stochastic Systems

arXiv: https://arxiv.org/abs/2511.17436 · HTML: https://mlsanity.com/paper/2511.17436/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 23 references that are in the map.
- First posted on arXiv 21 Nov 2025.

## Builds on (most cited first, 7 of 7)

- [Regret Bounds for Adaptive Nonlinear Control](https://mlsanity.com/paper/2011.13101/) (2020)
- [A Historical Perspective of Adaptive Control and Learning](https://mlsanity.com/paper/2108.11336/) (2021)
- [Robust adaptive MPC using control contraction metrics](https://mlsanity.com/paper/2209.11713/) (2022)
- [A robust adaptive model predictive control framework for nonlinear uncertain systems](https://mlsanity.com/paper/1911.02899/) (2019)
- [Learning-Based Adaptive Control for Stochastic Linear Systems with Input Constraints](https://mlsanity.com/paper/2209.07040/) (2022)
- [Stability Bounds for Learning-Based Adaptive Control of Discrete-Time Multi-Dimensional Stochastic Linear Systems with Input Constraints](https://mlsanity.com/paper/2304.00569/) (2023)
- [Is It Possible to Stabilize Disrete-time Parameterized Uncertain Systems Growing Exponentially Fast?](https://mlsanity.com/paper/1810.08128/) (2018)

## Abstract (arXiv)

We consider the adaptive control problem for discrete-time, nonlinear stochastic systems with linearly parameterised uncertainty. Assuming access to a parameterised family of controllers that can stabilise the system in a bounded set within an informative region of the state space when the parameter is well-chosen, we propose a certainty equivalence learning-based adaptive control strategy, and subsequently derive stability bounds on the closed-loop system that hold for some probabilities. We then show that if the entire state space is informative, and the family of controllers is globally stabilising with appropriately chosen parameters, high probability stability guarantees can be derived.