Robust controller design for systems with probabilistic uncertain parameters using multi-objective genetic programming

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.