## 4 Simulation Results and Analysis
\begin{table}
\begin{tabular}{c|c c}  & **Parameter** & **Value** \\ \cline{2-3}  & \(l_{1}\) (\(m\)) & 0.5 \\ Robotic manipulator & \(l_{2}\) (\(m\)) & 0.5 \\ \(m_{1}\) (\(kg\)) & 5 \\ \(m_{2}\) (\(kg\)) & 2 \\ \(g\) (\(m/s^{2}\)) & 9.8 \\ \hline \end{tabular}
\end{table} 
Table 1: Parameters of robotic manipulator. Figure 5: 2-rigid-link robotic manipulator. could increase the settling time. Therefore, the trial of selecting \(k_{yi}\) could start at a small value, and then users could decrease it until the converging rate of the tracking error is acceptable. \(\beta_{i}\) determines the converging rate of the auxiliary variable \(z_{i}\) that has a significant effect on steady state error in the controller [33]. However, in the proposed controller, the RL-based term is introduced to improve the tracking performance and thereby the effect of \(\beta_{i}\) is decreased. We suggest to offer \(\beta_{i}\) with a medium value ranging between 0.1-1. **Remark 14**. : _large values of \(\psi_{i}\) and \(\delta_{i}\) can lead to a fast adaption of \(\hat{d}_{i}\) to handle system uncertainty and external disturbance. However, the inappropriately large \(\psi_{i}\) and \(\delta_{i}\) could result in a sharp variation of \(\hat{d}_{i}\) and then a chattering effect on control torques. Therefore, the selection of \(\psi_{i}\) and \(\delta_{i}\) could start at a big value, and then users could decrease them until no chattering effect occurs on the control torques. Over-small values of \(\overline{\Omega}_{i}\) could lead to an insufficient decrease of \(\hat{d}_{i}\) that still brings up a chattering effect on control torques. Meanwhile, over-great values of \(\overline{\Omega}_{i}\) could negatively influence the robustness to uncertainty and disturbance. Hence, the selection of \(\overline{\Omega}_{i}\) could start at some small values, and then users could increase \(\overline{\Omega}_{i}\) until \(\hat{d}_{i}\) is significantly decreased at the final stage of the control to have a satisfactory chattering attenuation._  
**Remark 15**. : _Small/great values of \(\overline{\Phi}_{i}\) can amplify/reduce the effect of the RL term \(\Lambda_{i}\Lambda_{i}tanh\left(\frac{\varepsilon_{i}}{\overline{\Phi}_{i}}\right)\) in (10). The over-small values of \(\overline{\Phi}_{i}\) could result in the over-great magnitude of \(u_{i}\), while the over-great values of \(\overline{\Phi}_{i}\) could bring up an insufficient improvement on tracking performance. Therefore, the trial of selecting \(\overline{\Phi}_{i}\) is suggested to start at a great value, and then users could decrease \(\overline{\Phi}_{i}\) until a satisfying improvement on the tracking performance._  
According to Remark 11-Remark 15, the parameters of the proposed controller are selected in Table 2.  
Notably, it does not require an extensive trial to select parameters in Table 2 as the satisfying tracking performance is mainly obtained by the optimal \(\Lambda_{i}\) in the RL term \(\Lambda_{i}\Lambda_{i}tanh\left(\frac{\varepsilon_{i}}{\overline{\Phi}_{i}}\right)\). In other words, users can select some medium values for parameters (not optimal) in Table 2 by an acceptable amount of parameters-selection trails. Then, the fuzzy Q learning can automatically explore the \(\Lambda_{i}\) matching the selected parameters to have a satisfying tracking performance. **Remark 16**. : _Similar to [36], the parameters of membership function in (33) and (34), \(Lin(e_{i})=\left\{\zeta_{1,1}^{(i)},\,\zeta_{1,2}^{(i)},\ldots,\zeta_{1, \boldsymbol{\Delta}}^{(i)}\right\}\) and \(Lin\left(\hat{q}_{i}\right)=\left\{\zeta_{2,1}^{(i)},\,\zeta_{2,2}^{(i)}, \ldots,\zeta_{2,\boldsymbol{\delta}}^{(i)}\right\}\), are used to fuzzify \(e_{i}\) and \(\hat{q}_{i}\). To well present the \(e_{i}\) and \(\hat{q}_{i}\) in the form of firing rate, we suggest to offer \(\zeta_{1,1}^{(i)}\) and \(\zeta_{2,1}^{(i)}\) with some small values and provide some great values to \(\zeta_{1,\boldsymbol{\Delta}}^{(i)}\) and \(\zeta_{2,\boldsymbol{\delta}}^{(i)}\).