## 5 Discussion  
For the tracking control problem of a 2-DOF robot manipulator, we proposed a DNBC controller, which does not require any knowledge of the system since it uses a UKF-trained neural identifier, whose added value presents an optimization tuning via SI algorithms. Everyone tuned the initial filter parameters in an off-line simulation subsequently used in real-time experiments.  
Figure 9: Input torque link 2 with SI optimization. (**a**) Input torque link 2 ALO. (**b**) Input torque link 2 BA. (**c**) Input torque link 2 GWO. (**d**) Input torque link 2 MFO. (**e**) Input torque link 2 PSO.  
The selection of SI algorithms employed in this work is due to the following criteria:  
1. Few tuning parameters.
2. Good exploitation-exploration balance.
3. Low computational cost concerning their performance.  
The computational cost is the factor that we consider to be most important when carrying out the proposed optimization task, at least for the off-line simulation. Since the stochastic nature of both the UKF filter and the algorithms must be taken into account, in addition to the added cost of the controller, this translates into an increase in the number of attempts to achieve acceptable results. For this reason, Table 3 shows the average CPU time for each SI algorithm utilized.  
Interpreting the results obtained in the off-line simulation, we can highlight the following:  
1. According to Tables 2 and 3, all algorithms meet the selection criteria, have few parameters, acceptable performance, and relatively low CPU time.
2. All performance indices show similar average CPU time for each algorithm. The algorithm with the lowest average CPU time was BA, while the highest was ABC.
3. Based on the statistical mean and standard deviation, the best-performing algorithm overall was ALO, followed by BA, GWO, and MFO, in that order.  
In the case of real-time experiments, the principal selection criterion is to maintain joint torque limits. Only the Bolza form (3) and the objective function (4) of all performance measures consider the joint torques. Although Table 3 shows that all algorithms perform well, input torque signals in the simulation of the ABC, ACO, CS, APSO, and WOA algorithms exceeded the joint torque limits. For this reason, they were discarded from being used in real-time experiments.  
Interpreting the results obtained in real-time, we can reach the following final remarks:  
1. According to Figures 5-7, all algorithms perform better than the UKF without optimization. This demonstrates the advantages of using the proposed methodology. Table 4 shows the values of the objective function (4) evaluated in all used algorithms; the performance of these algorithms is reflected by minimizing the value of the objective function since it is described in terms of tracking and identification errors. As we can observe, the one with the best performance is the ALO, which we can also contrast in Figure 7. The controller performance shows a notorious improvement concerning a previous heuristic tuning.
2. Concerning Figure 5, the performance of the GWO for the first link is not up to par. However, according to Figure 6, this algorithm on the second link performs better than the other algorithms. Figure 9c exhibits this in the noise of the input torque signal, which is reflected in the RMS value in Table 5.