We propose a certainty-equivalence scheme for adaptive control of scalar linear systems subject to additive, i.i.d. Gaussian disturbances and bounded control input constraints, without requiring prior knowledge of the bounds of the system parameters, nor the control direction. Assuming that the system is at-worst marginally stable, mean square boundedness of the closed-loop system states is proven. Lastly, numerical examples are presented to illustrate our results.

翻译：针对具有加性独立同分布高斯扰动和有界控制输入约束的标量线性系统，我们提出了一种基于确定性等价原理的自适应控制方案，该方案无需系统参数边界或控制方向的先验知识。在系统至少保持临界稳定的假设下，证明了闭环系统状态的均方有界性。最后，通过数值算例对所提结果进行了说明。