持续激励在ARX自适应跟踪中的作用
On the usefulness of persistent excitation in ARX adaptive tracking
摘要：
持续激励的有用性在控制界是众所周知的。由于持续激励自适应跟踪控制，我们表明，它是可能的，以避免强可控性假设最近提出的多维ARX框架。我们建立了未知参数的最小二乘估计和加权最小二乘估计的几乎必然收敛。给出了中心极限定理和重对数重对数律。所有这些渐近分析都与适当的极限矩阵的Schur补有关。
英文摘要：
The usefulness of persistent excitation is well-known in the control community. Thanks to a persistently excited adaptive tracking control, we show that it is possible to avoid the strong controllability assumption recently proposed in the multidimensional ARX framework. We establish the almost sure convergence for both least squares and weighted least squares estimators of the unknown parameters. A central limit theorem and a law of iterated logarithm are also provided. All this asymptotical analysis is related to the Schur complement of a suitable limiting matrix.
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