A Framework for Adaptive Stabilisation of Nonlinear Stochastic Systems

• URL: http://arxiv.org/abs/2511.17436v1
• Date: Fri, 21 Nov 2025 17:33:00 GMT
• Title: A Framework for Adaptive Stabilisation of Nonlinear Stochastic Systems
• Authors: Seth Siriya, Jingge Zhu, Dragan Nešić, Ye Pu,
• Abstract summary: We consider the adaptive control problem for discrete-time, nonlinear systems with linearly parameterised uncertainty.<n>We propose a certainty equivalence learning-based adaptive control strategy, and derive stability bounds on a closed-loop system that hold for some probabilities.<n>We 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.
• Score: 10.266286487433584
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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