Occupation measures and linear matrix inequality (LMI) relax-ations (called the moment sums of squares or Lasserre hierarchy) have been used previously as a means for solving control law verification and validation (VV) problems. However, these methods have been restricted to relatively simple control laws and a limited number of states. In this document, we extend these methods to model reference adaptive control (MRAC) configurations typical of the aircraft industry. The main contribution is a validation scheme that exploits the specific nonlinearities and structure of MRAC. A nonlinear F-16 plant is used for illustration. LMI relaxations solved by off-the-shelf-software are compared to traditional Monte-Carlo simulations.

中文翻译：

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自适应控制验证的措施和 LMI

占用度量和线性矩阵不等式 (LMI) 松弛（称为平方矩和或 Lasserre 层次结构）以前已被用作解决控制律验证和验证 (VV) 问题的方法。然而，这些方法仅限于相对简单的控制律和有限数量的状态。在本文档中，我们将这些方法扩展到模拟航空工业典型的参考自适应控制 (MRAC) 配置。主要贡献是利用 MRAC 的特定非线性和结构的验证方案。非线性 F-16 设备用于说明。通过现成软件解决的 LMI 松弛与传统的蒙特卡罗模拟进行了比较。