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自适应控制算法的跟踪误差(实际输出与参考输出之差)是否趋向零与参数估计是否收敛到它的真值是不同的。一般地说,自适应系统的跟踪误差趋向于零并不一定有参数估计的一致性。本文在性能指标中同时考虑了估计精度与跟踪误差,用随机逼近的Robbins-Monro解导出其算法,并用Ljung的连带常微分方程理论证明了它的收敛性。
It is different whether the tracking error of the adaptive control algorithm (the difference between the actual output and the reference output) approaches zero and whether the parameter estimation converges to it. In general, the tracking error of adaptive systems tends to zero and does not necessarily have the consistency of parameter estimation. In this paper, both the estimation accuracy and the tracking error are considered in the performance index. The Robbins-Monro approximation algorithm is derived and the convergence is proved by Ljung’s theory of associated ordinary differential equations.