Optimal design of controllers without considering uncertainty in the plant dynamics can induce feedback instabilities and lead to obtaining infeasible controllers in practice. This paper presents a multi-objective evolutionary algorithm integrated with Monte Carlo simulations (MCS) to perform the optimal stochastic design of robust controllers for uncertain time-delay systems. Each potential optimal solution represents a controller in the form of a transfer function with the optimal numerator and denominator polynomials. The proposed methodology uses genetic programming to evolve robust controllers. Using GP enables the algorithm to optimize the structure of the controller and tune the parameters in a holistic approach. The proposed methodology employs MCS to apply robust optimization and uses a new adaptive operator to balance exploration and exploitation in the search space. The performance of controllers is assessed in the closed-loop system with respect to three objective functions as (1) minimization of mean integral time absolute error (ITAE), (2) minimization of the standard deviation of ITAE and (3) minimization of maximum control effort. The new methodology is applied to the first-order and second-order systems with dead time. We evaluate the performance of obtained robust controllers with respect to the upper and lower bounds of step responses and control variables. We also perform a post-processing analysis considering load disturbance and external noise; we illustrate the robustness of the designed controllers by cumulative distribution functions of objective functions for different uncertainty levels. We show how the proposed methodology outperforms the state-of-the-art methods in the literature.

在不考虑工厂动态不确定性的情况下优化控制器的设计会导致反馈不稳定，并导致在实践中获得不可行的控制器。本文提出了一种与蒙特卡洛模拟（MCS）集成的多目标进化算法，可以对不确定时滞系统进行鲁棒控制器的最优随机设计。每个潜在的最佳解都以具有最佳分子和分母多项式的传递函数的形式表示一个控制器。所提出的方法使用遗传编程来发展鲁棒的控制器。使用GP可以使算法优化控制器的结构并以整体方式调整参数。所提出的方法利用MCS进行鲁棒优化，并使用新的自适应算子来平衡搜索空间中的探索和开发。在闭环系统中，针对以下三个目标函数评估控制器的性能：（1）最小化平均积分时间绝对误差（ITAE），（2）最小化ITAE的标准偏差和（3）最小化最大控制努力。该新方法适用于具有停滞时间的一阶和二阶系统。我们针对阶跃响应和控制变量的上限和下限评估获得的鲁棒控制器的性能。我们还考虑了负载干扰和外部噪声进行了后处理分析。我们通过针对不同不确定性水平的目标函数的累积分布函数来说明所设计控制器的鲁棒性。我们将展示所提出的方法论如何胜过文献中的最新方法。