Motivated by the sliding mode control approach, a stochastic controller design methodology is developed for discrete-time, vector-state linear systems with additive Cauchy-distributed noises, scalar control inputs, and scalar measurements. The control law exploits the recently derived characteristic function of the conditional probability density function of the system state given the measurements. This result is used to derive the characteristic function of the conditional probability density function of the sliding variable, utilized in the design of the stochastic controller. The incentive for the proposed approach is mainly the high numerical complexity of the currently available method for such systems, that is based on the optimal predictive control paradigm. The performance of the proposed controller is evaluated numerically and compared to the alternative Cauchy controller and a controller based on the Gaussian assumption. A fundamental difference between controllers based on the Cauchy and Gaussian assumptions is the superior response of Cauchy controllers to noise outliers. The newly proposed Cauchy controller exhibits similar performance to the optimal predictive controller, while requiring significantly lower computational effort.

中文翻译：

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具有加性柯西噪声的线性系统的最大条件概率随机控制器

受滑模控制方法的启发，为具有加性柯西分布噪声、标量控制输入和标量测量的离散时间矢量状态线性系统开发了一种随机控制器设计方法。控制律利用给定测量值的系统状态的条件概率密度函数的最近导出的特征函数。该结果用于推导出滑动变量的条件概率密度函数的特征函数，用于随机控制器的设计。所提出方法的动机主要是此类系统当前可用方法的高数值复杂性，即基于最佳预测控制范式。所提出的控制器的性能进行了数值评估，并与替代的柯西控制器和基于高斯假设的控制器进行了比较。基于柯西和高斯假设的控制器之间的根本区别在于柯西控制器对噪声异常值的卓越响应。新提出的柯西控制器表现出与最优预测控制器相似的性能，同时需要显着降低计算量。