## 5 Conclusions and Future Developments  
In this paper, for a broad class of uncertain nonlinear MIMO systems, including many manufacturing systems and land, sea, and air transportation systems, a novel and unified robust control approach has been provided. It allows to design robust PD-type control laws without chattering to track a reference signal with bounded second derivative with the tracking error norm smaller than a prescribed value, despite the presence of bounded disturbances, parametric, and structural uncertainties, and bounded measurement noises. It has also been proved that the proposed control laws are robust with respect to bounded measurement noises.  
With reference to the mechanical and transportation systems, this theory has been successfully applied when the controller uses information signals related to the joint space or signals related  
Figure 40: Time histories of \(u,\ e\) for \(a=20\).  
Figure 39: Time histories of \(u,\ e\) for \(a=10\).  
to the workspace. Moreover, the proposed results have also been fruitfully used for the control of human-machine interaction.  
The obtained theoretical results have been illustrated through four relevant theoretical and engineering applications.  
The main advantages of the results of this study can be summarized as follows:  
* The considered class of nonlinear uncertain MIMO systems is broad and includes an important class of uncertain linear systems.
* A comprehensive approach based on the concept of majorant systems is provided to design smooth robust controllers. They have been used to track a generic reference signal with bounded second derivative with a tracking error norm smaller than a prescribed value.
* The obtained control laws are easy to design and implement. These laws have no high gains and are free from discontinuities.
* Suitable filtering laws are proposed for tracked trajectories to facilitate the implementation of the control laws and reduce the control magnitude, particularly during the transient phase.
* The maximum tracking error can be fixed a priori despite bounded parametric uncertainties, disturbances, and velocity measurement noise.
* A simple relation exists between a single design parameter of the controller and the maximum tracking error, which is useful for obtaining the desired tracking precision.
* The proposed control laws are robust with respect to bounded measurement noises.  
The established theoretical results can be used also to obtain further analysis and synthesis results and study complex systems with parametric and structural uncertainties. Moreover, other engineering and/or theoretical complex nonlinear uncertain systems can be easily controlled as the treated case studies, e.g., a drone and missile in the ongoing activity of the author.  
Future developments of this methodology and ongoing work of the author are: the theoretical extension of the proposed results when real derivative actions, real actuators and real amplifiers based on the PWM technique are considered.  
The following are available online at [[http://www.mdpi.com/2076-3417/8/11/2236/s1](http://www.mdpi.com/2076-3417/8/11/2236/s1)]([http://www.mdpi.com/2076-3417/8/11/2236/s1](http://www.mdpi.com/2076-3417/8/11/2236/s1)), An illustrative video of the robotic assembly system reported in Application 3 is provided. This video shows: (1) an operation of robotic assembly; (2) a human-robot interaction of spring-damper type; (3) a human-robot interaction of damper type.  
This work was supported by the Italian Ministry of Education, Universities and Research.  
The author is deeply grateful to Professor [PERSON], Senior Member of Automation group of the Department of Electrical Engineering and Information Technology, University of Naples Federico II, for his valuable encouragement and advice.  
The author declares no conflict of interest.