It is typically proven in adaptive control that asymptotic stabilization and tracking holds, and that at best a bounded-noise bounded-state property is proven. Recently, it has been shown in both the pole-placement control and the $d$-step ahead control settings that if, as part of the adaptive controller, a parameter estimator based on the original projection algorithm is used and the parameter estimates are restricted to a convex set, then the closed-loop system experiences linear-like behavior: exponential stability, a bounded gain on the noise in every $p$-norm, and a convolution bound on the exogenous inputs; this can be leveraged to provide tolerance to unmodelled dynamics and plant parameter time-variation. In this paper, we extend the approach to the more general Model Reference Adaptive Control (MRAC) problem and demonstrate that we achieve the same desirable linear-like closed-loop properties.

中文翻译：

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具有类线性闭环行为的模型参考自适应控制

通常在自适应控制中证明渐近稳定和跟踪成立，并且充其量证明了有界噪声有界状态属性。最近，在极点放置控制和 $d$-step 超前控制设置中都表明，如果作为自适应控制器的一部分，使用基于原始投影算法的参数估计器并且参数估计受到限制到凸集，则闭环系统会经历类似线性的行为：指数稳定性，每个 $p$-范数中噪声的有界增益，以及外生输入上的卷积边界；这可以用来提供对未建模动力学和工厂参数时间变化的容忍度。在本文中，