Recently, a Lyapunov design of least-squares model-reference adaptive control (LS-MRAC) has been proposed. Unlike other least-squares based algorithms, the update law is driven only by the tracking error and, in this way, it does not require normalization or parameter projection to assure stability of the closed-loop system. Moreover, the algorithm has striking improved tracking error transient and superior parameter convergence properties when compared with a conventional MRAC. Also recently, a new design employing high-order parameter tuners has been proposed. In this design, the parameter derivatives are quite easily and systematically obtained. A key point of the procedure is the Lyapunov function used for the analysis that explicitly considers the derivatives of the parameter. The implementation of the algorithm requires finding a symmetric positive definite matrix such that a is negative definite. This is a fundamental property to assure its stability. The solution to this problem leads to a novel simple proof for the equivalence between the Routh–Hurwitz stability criterion and the Lyapunov’s method. In this work both design methodologies are combined, that is, the LS-MRAC algorithm is redesigned with high-order tuners.

中文翻译：

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具有高阶参数调谐器的最小二乘模型参考自适应控制

最近，提出了最小二乘模型参考自适应控制（LS-MRAC）的李亚普诺夫设计。与其他基于最小二乘的算法不同，更新律仅由跟踪误差驱动，这样，它不需要归一化或参数投影来确保闭环系统的稳定性。此外，与传统的MRAC相比，该算法具有显着改善的跟踪误差瞬态和优越的参数收敛特性。最近，还提出了一种采用高阶参数调谐器的新设计。在该设计中，参数导数很容易且系统地获得。该过程的关键点是用于分析的 Lyapunov 函数，该函数明确考虑了参数的导数。该算法的实现需要找到一个对称正定矩阵，使得 a 是负定的。这是确保其稳定性的基本属性。这个问题的解决导致了劳斯-赫尔维茨稳定性准则和李亚普诺夫方法之间等价性的新颖简单证明。在这项工作中，两种设计方法相结合，即用高阶调谐器重新设计 LS-MRAC 算法。