## 1 Introduction
The proposed control system achieved 85.71% success in withstanding external forces, but did not consider its suitability for under-actuated systems. Although [PERSON] et al. [16] implemented Interval Type-2 Fuzzy Logic Control (IT2 FLC) to a triple inverted pendulum on two wheels and the developed controller managed to withstand 16% greater disturbance than the type-1 fuzzy logic controller, the researchers considered disturbance applied on the third link only. The control system's robustness against possible disturbances on other links is missing in the study. Since optimization provides enhancements in control system design, it has been employed in different ways to provide optimal solutions for engineering problems. [PERSON] et al. (2017), for instance, presented optimal fuzzy SMC for a two-DOF robotic manipulator. In order to compensate for the information shortages with respect to the system's uncertainties, PSO was used to adjust the parameters of fuzzy membership functions. The proposed control method outperformed the classic SMC in terms of control input smoothness, though it had slightly higher tracking errors. The two-DOF robotic manipulator has also been controlled by an optimal integral SMC based on the pseudo spectral method. [PERSON] et al. (2018) applied integral SMC to restrain disturbance and adopted the pseudo spectral method to deal with the constraints. The proposed controller demonstrated the ability to track the desired reference signals accurately within 2 s. The results illustrated that the robotic manipulator system exhibited good robustness and anti-disturbance capabilities when subjected to external disturbances. However, the measurement noise for the system has not been considered. [PERSON] et al. (2019) used Grey Wolf Optimization (GWO) with chaotic basis to tune the parameters of a higher-order SMC for the position control of a two-DOF rigid robot manipulator. Tent and Singer maps were applied to the optimization method to balance the exploration/exploitation phases of the algorithm, based on the algorithm itself and the chosen cost function. It was shown that the general repeatability of the algorithm was improved using chaotic maps in the higher-order SMC optimization. However, the suitability of the proposed method has not been tested for three-DOF manipulators. For the electro-hydraulic actuator system, [PERSON] et al. (2019) applied PSO to tune the Proportional-Integral-Derivative (PID) sliding surface of the SMC. The use of optimization in controller design has improved the system's performance by 0.6407%. However, uncertainty was not taken into consideration in the study. On the other hand, [PERSON] et al. (2018) used a Linear-Quadratic Regulator (LQR), where the cost is defined through a quadratic function, and pole placement, where the closed-loop poles of the plant are positioned in desired locations in the s-plane. Both control methods were applied for the stabilization of a triple inverted pendulum system and compared; the comparison shows that the pole-placement controller improves the stability of the system more, but with no indications of its robustness against perturbations. As for the triple-link rotary inverted pendulum, [PERSON] et al. (2018) made a comparative study of the Neuro-Fuzzy Friction Estimation Model (NFFEM) and Adaptive Friction Estimation Model (AFEM) methods used to estimate the friction coefficients of the plant. The NFFEMs are trained by a radial-basis function artificial neural network. It has been deduced, based on the root mean square error of the joints' position, that NFFEMs produce much better estimation results than AFEMs, although the researchers had not address the robustness issue. [PERSON] et al. (2019) applied H\({}_{\infty}\) and \(\mu\)-synthesis control for the double inverted pendulum on a cart to achieve disturbance rejection and robust stability.