**8. Conclusions**

In this study, a motion controller was developed and investigated for a WRK system to obtain an appropriate output trajectory tracking performance. The designed controller showed its ability to perform without errors against model uncertainties and external disturbances. The designed control algorithm includes the adaptive law, a RBF NN compensator, and a robust feedback part. The adaptive law is applied to supply the feedback controller with the estimation of RBF NN weights by updating the weights of the RBF NN compensator. The robust feedback controller tracks the desired trajectory in the presence of uncertainties. All the uncertainties are considered in the WRK dynamics using the Lagrange approach. The *L*2 gain technique facilitates the control motion solutions and provides the feature of intelligent WRK control. The stability is proved by applying an HJI approach based on the optimization technique and Lyapunov stability theory. The presented robust RBF NN algorithm ensures the ability to implement the adaptive controller easily as well as the stability of the WRK system. The results demonstrate that the designed WRK controller can be successfully implemented when the parameter values are modified to accommodate the potential user of the device. As a future work, it is recommended to apply the obtained control of this study practically to a real WRK device. A deep learning approach is recommended as a way to enhance the performance of RBF NNs. Furthermore, the implementation of advanced meta-heuristic optimization techniques is a promising future area of study.

**Author Contributions:** Conceptualization, H.J., I.A.-D., G.T., L.L. and M.O.; Methodology, H.J., I.A.-D., G.T., L.L. and M.O.; Software, H.J., I.A.-D. and G.T.; Validation, I.A.-D. and G.T.; Formal analysis, H.J., I.A.-D., G.T., L.L. and M.O.; Investigation, H.J., I.A.-D., G.T., L.L. and M.O.; Resources, H.J., I.A.-D., G.T. and M.O.; Data curation, I.A.-D., G.T. and M.O.; Writing—original draft, I.A.-D. and H.J.; Writing—review & editing, I.A.-D. and H.J.; Visualization, I.A.-D.; Supervision, H.J., I.A.-D., G.T., L.L. and M.O.; Project administration, H.J., I.A.-D., G.T., L.L. and M.O.; Funding acquisition, H.J.,L.L.andM.O.Allauthorshavereadandagreedtothepublishedversionofthemanuscript.

**Funding:** This research work was funded by Institutional Fund Projects under gran<sup>t</sup> no. (IFPIP 344-135-1443). The authors gratefully acknowledge technical and financial support from the Ministry of Education and King Abdulaziz University, DSRJeddah, Saudi Arabia.

**Data Availability Statement:** Data are contained within the article.

**Conflicts of Interest:** The authors declare no conflict of interest.
