Classical discrete-time adaptive controllers typically provide asymptotic stabilization and tracking; usually the affect of the noise is at best bounded-input bounded-output. Recently we have shown that if you design a discrete-time adaptive controller in just the right way, then in a variety of situations you not only obtain exponential stability, but also a bounded gain on the noise in every p−norm, as well as a never-before-seen linear-like convolution bound on the input–output behavior. Quite surprisingly, the approach is very natural, and relies on the use of the unmodified, original projection algorithm to carry out parameter estimation; if the set of plant uncertainty is not convex, then a multi-estimator and switching are used. The goal of this paper is to provide an overview of the approach, discuss the results-to-date, and list some of the open problems.

中文翻译：

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在自适应控制设置中自然出现类似线性的特性

经典的离散时间自适应控制器通常提供渐近稳定和跟踪；通常，噪声的影响充其量是有界输入有界输出。最近我们已经证明，如果你以正确的方式设计一个离散时间自适应控制器，那么在各种情况下，你不仅可以获得指数稳定性，而且每个p 中的噪声都有界增益-范数，以及输入-输出行为上从未见过的线性卷积边界。令人惊讶的是，该方法非常自然，并且依赖于使用未经修改的原始投影算法来进行参数估计；如果工厂不确定性集合不是凸的，则使用多估计器和切换。本文的目标是提供该方法的概述，讨论迄今为止的结果，并列出一些未解决的问题。