未知控制方向的简单线性对象间接自适应跟踪系统的稳定性分析（英文）

Stability Analysis of Indirect Adaptive Tracking Systems for Simple Linear Plants with Unknown Control Direction

本文研究一类一阶线性连续时间对象的自适应跟踪器,并给出不同估计量和修正确定性等价控制律.我们克服了确定损失的困难(或控制)的系统增益的估计值是零,纠正了米德尔顿和Kokotovic的文章(1992)对上述对象的间接自适应调节的一些实质性的错误的结果.在构建的自适应跟踪系统中,得到相平面轨迹或完全描述闭环系统的非线性行为的显式解的显式表达式,并对所设计的自适应跟踪系统可能由损失估计模型的稳定性所带来问题进行分析.讨论了这些结果对高阶线性连续时间对象的间接自适应跟踪情况的影响.同时通过类似的模式讨论了未知的控制方向和模型参数.

The paper deals with the adaptive tracker for a class of first-order linear continuous-time plants, with different estimators and modified certainty-equivalence control law. We overcome the difficulty of the loss of stabilizability (or controllability) as the estimate of the plant gain is zero and correct a few substantive mistakes of the results from Middleton and Kokotovic’s paper (1992) about the indirect adaptive regulation of the above-mentioned plant. In the constructed adaptive tracking systems, the explicit expression for the phase-plane trajectories or the explicit solution completely describing the nonlinear behavior of the resultant closed-loop systems is obtained, and some problems of the designed adaptive tracking systems, which due to a loss of stabilizability of the estimated model probably are analyzed. The paper also discusses the impact of these results for the indirect adaptive tracking case of higher order linear continuous-time plants. Meanwhile, we discuss the unknown both control direction and model parameters by making use of the similar pattern.