This paper aims to make a trade‐off between performance and robustness in stochastic control systems with probabilistic uncertainties. For this purpose, we develop a surrogate‐based robust simulation‐optimization approach for robust tuning and analyzing the sensitivity of stochastic controllers. Kriging surrogate is combined with robust design optimization to construct a robust simulation‐optimization model in the class of dual response surfaces. Randomness in simulation experiments due to uncertainty is analyzed through bootstrapping technique by computing confidence regions for the estimation of Pareto frontier. Results confirmed a proper trade‐off between the model's performance with the measure of expected Integral Squared Error (ISE) and robustness against uncertainty in the plant's physical parameters. Finally, the proposed method is evaluated in terms of accuracy, computational cost, and simplicity particularly in comparison with some common existed techniques in the tuning of the Proportional‐Integral‐Derivative (PID) and Fractional‐Order PID (FOPID) controllers.

中文翻译：

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随机整数和分数阶PID控制系统的鲁棒调节和灵敏度分析：基于代理的鲁棒仿真优化

本文旨在在具有随机不确定性的随机控制系统中，在性能和鲁棒性之间做出权衡。为此，我们开发了一种基于代理的鲁棒仿真优化方法，用于鲁棒调整和分析随机控制器的灵敏度。Kriging代理与稳健的设计优化相结合，在双响应曲面类别中构建了稳健的仿真优化模型。通过自举技术，通过计算置信区域以估计帕累托边界，分析了由于不确定性导致的仿真实验中的随机性。结果证实了模型的性能与预期的积分平方误差（ISE）的度量之间的适当权衡，以及针对工厂物理参数不确定性的鲁棒性。最后，