A Framework for Adaptive Stabilisation of Nonlinear Stochastic Systems
This work addresses stability in adaptive control for nonlinear stochastic systems, which is an incremental advance in control theory.
The paper tackles the adaptive control problem for discrete-time nonlinear stochastic systems with linearly parameterised uncertainty by proposing a certainty equivalence learning-based adaptive control strategy, and it derives stability bounds on the closed-loop system that hold with certain probabilities, showing that high probability stability guarantees can be achieved under specific conditions.
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.