Maximum Conditional Probability Stochastic Controller for Linear Systems with Additive Cauchy Noises
Maximum Conditional Probability Stochastic Controller for Linear Systems with Additive Cauchy Noises
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DOI：
10.1007/s10957-020-01735-5
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发表时间：
2020-08
影响因子：
1.9
通讯作者：
Nati Twito;M. Idan;J. Speyer
中科院分区：
文献类型：
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作者：
Nati Twito;M. Idan;J. Speyer
受滑模控制方法的启发，针对具有Cauchy分布噪声、标量控制输入和标量测量的离散时间向量状态线性系统，提出了一种随机控制器设计方法。该控制律利用了最近导出的测量系统状态的条件概率密度函数的特征函数。这一结果是用来推导的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。所提出的方法的动机主要是高数值复杂性的目前可用的方法，这样的系统，这是基于最优预测控制范式。所提出的控制器的性能进行了数值评估，并比较替代柯西控制器和基于高斯假设的控制器。基于柯西和高斯假设的控制器之间的根本区别是柯西控制器对噪声离群值的上级响应。新提出的柯西控制器表现出类似的性能的最优预测控制器，而需要显着降低计算工作量。
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.