发表机构
Central University; Center for Engineering Systems and Sciences; Sirius University of Science and Technology（中央大学; 工程系统与科学中心; 天狼星科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出将参数化评判器作为李雅普诺夫候选函数，通过投影到可行速度集与衰减半空间交集实现自适应稳定，并给出可行性检验与反例，在力受限小车-杆上验证了条件稳定机制。
AI 中文摘要
我们研究已知控制仿射系统的自适应稳定，通过将当前参数化的评判器本身视为李雅普诺夫候选函数。其全导数包含一个参数速度项，可补偿不利的状态演化。将投影作用于有界可行速度集与一个衰减半空间的交集上，可同时保证参数不变性和李雅普诺夫下降。我们给出了精确的点态可行性检验、一个条件状态稳定性定理，以及一个反例，说明包含稳定成员的正评判器族并不蕴含持续可行性。一个凸端点约束提供了不同的采样实现。一种带有局部Riccati锚点的通用周期多项式因子评判器，在无机械能特征、无回放训练、无路点、无控制器切换的力受限小车-杆系统上进行了评估。冻结控制器在两组共600个采样初始状态上通过了稳定性和数值衰减检查；400条匹配的连续轨迹也通过。独立的再积分审计和保守的局部可行性证书与全局或机器算术保证相区分。与非线性模型预测控制相比，所测实现使用更少的CPU，但代价、稳定时间和小车行程更高。结果支持一种条件自适应稳定机制。
英文摘要
We study adaptive stabilization of known control-affine systems by treating the current parameterized critic itself as a Lyapunov candidate. Its total derivative contains a parameter-velocity term that can compensate unfavorable state evolution. A projection onto the intersection of a bounded admissible velocity set and one decay halfspace enforces parameter invariance and Lyapunov decrease simultaneously. We give an exact pointwise feasibility test, a conditional state-stability theorem, and a counterexample showing why a positive critic family containing a stabilizing member does not imply persistent feasibility. A convex endpoint constraint provides a distinct sampled implementation. A generic periodic polynomial-factor critic with a local Riccati anchor is evaluated on a force-limited cart-pole without mechanical-energy features, replay training, waypoints, or controller switching. The frozen controller passes stabilization and numerical decay checks on 600 sampled initial states across two draw sets; 400 matched continuous trajectories also pass. Independent reintegration audits and a conservative local feasibility certificate are distinguished from a global or machine-arithmetic guarantee. Compared with nonlinear model-predictive control, the measured implementation uses less CPU but has higher cost, settling time, and cart travel. The results support a conditional adaptive stabilization mechanism.
