Abstract

The aim of the present paper is to synthesize an adaptive control system with variable adaptation-loop gain to compensate for the plant parametric uncertainty. In contrast to the existing ones, such a system simultaneously (1) includes an algorithm for the automatic calculation of the parameter adjustment law gain in the controller, which operates in proportion to the current regressor value, thus permitting one to obtain an adjustable upper bound for the rate of convergence of the plant output–controller parameter errors to zero (subject to the condition of persistent excitation of the regressor); (2) does not require knowing the signs or values of the entries of the plant gain matrix. The Lyapunov second method and the recursive least squares method are used to synthesize such a control system. For this system, the stability and the boundedness of the above-mentioned error values are proved, and estimates for the rate of their convergence to zero are obtained. The efficiency of our approach is demonstrated by mathematical modeling of an example of a plant corresponding to the statement of the research problem.

中文翻译：

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基于递推最小二乘方法的变调整律增益自适应控制系统

摘要

本文的目的是合成具有可变自适应环路增益的自适应控制系统，以补偿设备的参数不确定性。与现有系统相反，这种系统同时（1）包括一种用于自动计算控制器中参数调整定律增益的算法，该算法与当前回归值成比例运行，从而允许获得可调整的上限工厂输出-控制器参数误差的收敛速度为零（取决于回归器的持续激励条件）；（2）不需要知道植物增益矩阵的项的符号或值。使用李雅普诺夫第二方法和递推最小二乘法来综合这种控制系统。对于这个系统，证明了上述误差值的稳定性和有界性，并获得了收敛到零的估计值。通过对与研究问题陈述相对应的植物示例进行数学建模，可以证明我们方法的有效性。