 Hello everyone. Welcome to the NPTEL on non-linear adaptive control. I am Srikanth Supabhat from Systems and Control IIT. So in non-linear adaptive control, we are essentially talking about a sub area of non-linear control which has gained a lot of popularity in real applications such as fighter planes, satellites, drones and deep neural networks. So we want to understand what is it that is sort of being done in adaptive control which is different from conventional non-linear control. So if you look at a standard block diagram for an adaptive controller, what you find is that you have plant dynamics which consist of uncertainties in the form of terms such as lambdas and mews and these are characterized by uncertain parameters. Now in a conventional non-linear controller you would ignore these parameters or you would not be able to do any particular design against these parameters but in an adaptive controller you add a parameter identifier block which helps you to add a sort of robustness but not just robustness. It allows you to achieve tracking in the presence of these uncertain parameters also and essentially we are able to achieve precise tracking using such parameter identifier based adaptive controllers. So why do we want to have these parameters identifiers or why do we have such uncertainties? One of the first reasons is because of modeling issues. So typically you have a rather complex real-world system like what you see here in this picture but we simplify the model so that we can actually make the control and the design problem tractable and now in order to do these we have to make certain approximations which leads to uncertainties and unknowns in the system in the form of parameters. The next sort of uncertainty comes from the deployment of the system which is when you actually start using the system or operating the system there may be sensors which are trying to measure certain variables and there may be errors in these variables and in order to compensate for these errors also you need some kind of a special control algorithm which is where the adaptive control comes in. Now another kind of operational variation is because of you know incidents or accidents for example if a drone is flying and it means with an accident which doesn't completely damage it but say for example damages its propellers like you can see here and this results in a shape change which of course leads to changes in the parameters of the system and these new parameters are unknown to the you know the ground station that is actually flying this or operating this machine so what adaptive control does is provide as a means of actually compensating for these shape changes also. If you're using a very traditional fixed gain controller then one would require very very conservative and gains in order to provide robustness to the system to these sort of errors which are typically characterized as disturbances but certain errors especially measurement errors are non-disturbances and they even scale with the control magnitude and therefore adaptive control does not actually just give robustness but it attempts to identify these parameters also in addition to giving and or recovering ideal performance and this is why adaptive controllers have been one of the most popular real flight controllers in the industry in fact for fighter jets there is already been implementations of adaptive controllers and most of us already know about deep learning neural networks which is basically an adaptive controller which is trying to learn functions using training data so I hope that this journey on adaptive controller with me will be an exciting one and we will actually see how to get from theory to application of adaptive control real world. Thank you.