提出自适应控制框架，实现非线性随机系统的稳定调节。
A Framework for Adaptive Stabilisation of Nonlinear Stochastic Systems
- 基于确定性等价学习策略设计控制器。
- 在特定概率下保证闭环系统稳定性。
- 适用于状态空间全信息场景下的高概率稳定控制。
针对离散时间、非线性随机系统中线性参数化不确定性问题，假设存在一个参数化控制器族，在状态空间的可识别区域中，当参数选择得当时，可使系统在有界区域内稳定。本文提出一种基于确定性等价的学习型自适应控制策略，并推导出在某些概率下闭环系统稳定的边界。进一步证明，若整个状态空间均具有信息性，且控制器族在适当参数下全局稳定，则可获得高概率的稳定性保证。
原文摘要 · Abstract (English)
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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