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.

翻译：本文研究具有线性参数化不确定性的离散时间非线性随机系统的自适应控制问题。假设存在一个参数化控制器族，当参数选择恰当时，能够在状态空间信息丰富区域的有界集合内镇定系统，我们提出一种基于确定性等价学习的自适应控制策略，并推导出闭环系统在特定概率下成立的稳定性界。进一步证明，若整个状态空间均具有信息性，且控制器族在适当选取参数时具有全局镇定能力，则可获得高概率稳定性保证。