自适应确定性等价控制与调节触发有限时间最小二乘识别，第二部分：分析
Adaptive Certainty-Equivalence Control With Regulation-Triggered Finite-Time Least-Squares Identification, Part II: Analysis
AI总结：
本文分析了新的调节触发自适应控制方法的稳定性，提出了检查参数可观测性假设的算法，适用于每个微分方程中最多出现一个未知参数的非线性控制系统。
摘要：
我们提出了新调节触发自适应控制方法的稳定性分析，该方法在 companion paper 中引入。由于闭环系统是混合的，我们的证明与传统自适应控制证明有本质区别，其中Lyapunov分析要么涵盖完整的闭环状态，要么通过比较或Gronwall-Bellman引理分步进行。此外，我们提出了一种方便的算法来检查我们的参数可观测性假设，该算法涉及适当向量场的重复Lie导数，并可应用于每个微分方程中最多出现一个未知参数的非线性控制系统类。
英文摘要：
We present the stability analysis for the new regulation-triggered approach to adaptive control introduced in a companion paper. Due to the fact that the closed-loop system is hybrid, our proofs have essential differences from the conventional adaptive control proofs, where the Lyapunov analysis either encompasses the complete closed-loop state or is done in multiple steps through comparison or Gronwall-Bellman lemmas. In addition, we present a convenient algorithm for checking our parameter-observability assumption, which involves repeated Lie derivatives of appropriate vector fields and can be applied to the class of nonlinear control systems for which at most one unknown parameter appears in each differential equation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
