 Welcome to the NPTEL course on non-linear control design. I am Srikanth Sukumar from Systems and Control IIT Bombay. This course is primarily designed for beginning graduate students who have some exposure to linear systems, state space and so on. One of the first questions that comes to mind is why non-linear control? And the answer is rather too obvious. Almost every system that we see around us are non-linear systems. For example, here you see a non-holonomic mobile robotic system like a network of mobile robots. Here you see a satellite in orbit, here you see a smart grid network. You can see, you know, a virus or infection spread models. You can see aerial manipulators, quadrotors and even biological systems such as the beating of the heart. Now all of these are in fact non-linear systems. And if you want to manipulate the behavior of any of these, say using medication for the heart or using, you know, electrical supply for the smart grid or using some kind of medication or disease control mechanism for infection spread or using thrusters for satellites, the entire purpose of doing any modification in the behavior of the system is achieved via non-linear control. So what are the elements of non-linear control? So these are the kind of things that we will cover in this course. And there are three distinct components. The first is the analysis component where you have, you know, this Lyapunov theorem, the idea of stability in the sense of Lyapunov. Then we have notions such as the invariance theorems, which have slightly wider application to limit cycle behavior and things like that. And then we also study Babalat's lemma for time varying systems. So once we have a good basis, good background in the analysis of non-linear systems to study their stability and other asymptotic properties, we actually move on to the design, right? And what are the methods of design? These are only very, very, this is not an exhaustive list, but obviously given the constraints of time and so on. This is the sort of design methods we will look at in this course. It includes control Lyapunov functions-based design, back-stepping and integrator back-stepping, passivity-based design and feedback linearization, which in itself is another very, very large diverse area. There are also advanced design methods. We will look at some of those, the first being constrained control. So if you want your control system to have some kind of safe behavior that it doesn't collide or it doesn't, if it's interacting with humans, it doesn't hurt them, then you are in the domain of constrained control, state constrained control and so on. And so that is one of the new and upcoming areas. Then of course there is adaptive control when you have uncertainties and unknowns in the system. And there is the notions of finite time and sliding mode control which have these disturbance rejection like properties, right? So these are all the ingredients that will go into what we look at in this course. Now where, what kind of applications are there for control, non-linear control? So these are, I mean obviously again I cannot provide an exhaustive list here, but these are some of the applications that we ourselves work in our laboratory. The first that you see is synchronization of coupled outputs and this is applied to vehicle platooning, which is a very, very important application in transportation systems. Then there is network adaptive identification of, and control. So if you have some uncertainties in the network like bias affecting your sensor measurements, then how do you address these? How do you identify these bias over a network? So this becomes a non-linear adaptive control problem and we study it in such a framework. Then of course, non-linear control feeds into non-linear and geometric state observers for such aerial vehicles. And of course, for aerial motion simulators like this, you know, two-dough rotary aerobot that we have made in our own laboratory and this flapping wing aerobot, these are all systems where non-linear control is naturally applied to, yeah? So overall, I hope that this course will be a very interesting introduction into the very, very large domain of non-linear control. And I hope to see all of you coming in enthusiastically doing well in the course. And of course, most importantly, eventually applying it to some domain of your own expertise, be it defense, be it aerospace, be it electrical networks, and so on and so forth. Thank you.