hello everyone I am very pleased to kick off these new lecture series on adaptive control and learning I have been working on adaptive control more than a decade right now my PhD is on adaptive control and as a professor I had a chance to work on adaptive control research with a lot of agencies National Science Foundation NASA Air Force DARPA to name but a few examples and I had a chance to implement adaptive control on many exciting systems including NASA airstar and many other vehicles and I wanted to make a new lecture series on adaptive control and learning theory and this is kind of the introduction video but I want to well understand why we care about adaptive control so that's the purpose of this video to begin with without an exception this is a very important sentence a very important beginning without an exception every physical system is subject to disturbances and or uncertainties you can take a quadcopter or a multirotor system as an example it is subject to winds turbulence you can take a robotic arm ground robot it is subject to friction or let's say you are linearizing a system around an equilibrium point when you deviate from the takeaway Point your system will be subject to uncertainties resulting from this linearization process or simply you may have unknown parameters in the system or you may incorrectly estimate some parameters or let's say you are doing an operation um your actuator is subject to icing or let's say you have a structural damage your system May sub may be subject to degraded modes of operation and simply forget about everything you assumed you ignored Electronics you ignored some moment of inertia some changes in Mass based on some idolized assumptions all of them acting as your system as disturbances and or uncertainties well these disturbances are on and uncertainties most of the time negatively impact the desired stability and performance of your physical system in control so you need to deal with them I would like to give you the world's one of the simplest examples to understand uncertainties how they pop up I would like to consider Mass Supreme temper system we have a card here with mass m we have a spring with constant Alpha and damper with constant beta and P is the position of this card U is the applied control signal and let's say we would like to design a form of control algorithm not necessarily adaptive now I apologize for my voice so first of all when you model that system let's say you are using free body diagram right these forces resulting from Spring and damper negative effect your mass and your control signal will contribute will make the your system move along this um P meters now if you look at Newton's Second Law which is nothing but M A equals to the applied sum of Applied forces we have control force and this negative force due to the spring and others negative force due to the damper and this is your ma now you need to represent this system in state space for this let's call X1 SP second state is p Dot then X1 that becomes P dot which is X2 right X1 that equals P dot but P dot is X2 you have this so this is the first state X2 Dot is nothing but P dot dot and P dot that is here basically take this m put it here and 1 over m to the right hand side and replace pivot X1 P dot with X2 because this is what we defined then you arrive this equation now if you know Mass Alpha and beta let's say you know everything about that system then resulting State space will have this a matrix and B Matrix and if you know everything then you can use um any method for feedback purposes now let's say the let's consider a worst case scenario let's say you don't know Mass Alpha and beta you know nothing about your system then we move basically these unknown parameters outside our state space in the following sense that I highlight here first of all I empty my a matrix I moved these uncertain parameters like this outside here W is basically unknown weight w stands for weight and here I emptied B Matrix I moved Lambda 1 over M outside so this Lambda basically is called um unknown control Effectiveness metrics metrics in this case it's a scalar but in general it can be metrics and W as I mentioned is nothing but unknown weight this particular parametrization will be important later I don't want you to remember this um before the following videos but the point that I'm I am trying to make now since nothing is known about this system I need to live with this A and B matrixes and somehow I need to design the control signal to suppress or cancel the effect of Lambda uncertainty and W uncertainty and of course you can have let's say message known Alpha Beta unknown you can have um something between these systems so we need to parameterize basically you could you need to include the non parameters of the system inside these and leave others outside all right let's move forward so we have this unknown system to deal with we have in control theory two common approaches one of them is robust control method and the other one is adaptive control method what methods are well established and well respected methods in dealing with uncertainties in systems I would like to compare them and this will be a honest compression comparison first of all with robust control the resulting control algorithm will have fixed parameters they will be fixed however in adaptive control the resulting parameters of the controller will change in real time in robust control one more time when we tune control parameters we tune to a worst case scenario which may never happen in practice on the other hand with adaptive control we don't basically tune to a worst case scenario basically we let the control parameters change in real time to adapt to the changes in the physical system we'll learn from the basically we learn uncertainties and cancel their effect in real time and to design robust control methods we need to know upper bonds and lower Bonds on system uncertainties or the basically this W for example and Lambda terms on the other hand adaptive control we do not necessarily adaptive contract architectures do not necessarily excessively rely on models or these bounds and in robust control basically if we trade of performance versus uncertainty this means that if basically you have a lot of uncertainty it it is very hard to achieve a desired level of system performance however adaptive control with proper learning no such there is no such a trade-off and I would like to emphasize here proper learning well if you use most of the Adaptive controls from textbooks their performance will be unpredictable and this is one of the key reasons some people especially who has less understanding of adaptive control methods made divert from using the Adaptive control architectures however when you really understand the fundamental really understand what's going on and really understand how to well tune and well structure the proper learning algorithm for the active controllers you will see that they are way to go okay and robust control methods are generally linear and since they are linear they are their properties are well understood or you know over the entire literature however with adaptive control they basically adaptive control algorithms are inherently non-linear and because of their nonlinear structures sometimes people are scared of them and because of the nonlinear structures their properties are not very well understood now good news for you based on my extensive experience applications of adaptive control and learning theory in this new lecture series I will teach you all the important stuff and I mean it all the important stuff to understand adaptive control you are and learning algorithms you are going to understand you are going to understand different types you are going to understand uncertainty types and how to design properly these learning algorithms and um my vision for these new lecture series on adaptive control and learning is that this will be the best absolutely the best lecture Series in the YouTube in terms of I will put my all knowledge in adaptive control all right what about the textbooks or some references um on the left um this is a great book written by Boeing researchers Eugene lavresca and Kevin Weiss uh in fact Eugene laresky was one of my committee members during my PhD defense and I really respect his knowledge likewise Kevin wise I am acting together on different technical Committees of a I double A and either play and I if I recommend a book I would recommend this book on adaptive control it covers the material um in a well-rounded shape and to make a brief introduction or a jumpstart adaptive control I would like to recommend my Wiley Encyclopedia of electrical and electronics engineering article published in 2019 so-called model reference adaptive control you will this is not a survey paper or it is not intended to be a survey paper but I try to cover the state of the art as of 2019. um of course learning theory and adaptive control is a very Dynamic field and right now we are in 2023 a lot of stuff going on but in these videos I will try to capture all the basics textbook level adaptive control and the state of the art so what do you what you should learn before watching these new lecture series on adaptive control and learning well if you know linear Control Systems well with an understanding of leopono theory you should start watching the following videos that I will upload if you want to refresh your knowledge I will strongly recommend that go to my YouTube web page click to playlists find the playlist on lectures or on Advanced Control Systems I strongly recommend that you watch all the videos these are basically short videos and I try to coordinate my knowledge on important topics but if you are under time pressure and you you know you can you ask well which video should I watch first then I would recommend watch from the modeling part watch State space representations in fact when I was discussing uh um Sprint Mass damper system in the following like a couple of minutes ago I basically use a state space representation from the stability part you need to watch leopono stability and more and eigenvalues and more these are pretty important videos and from the control part you should watch State and output feedback of output feedback it should be here control of linear systems pole eigenvidia placement optimal linear quadratic control and model reference adaptive control so basically I have an Adaptive control video there already but it is short and you know the purpose of this lecture series is to dive into the detail do I am not going to stay at the textbook level I will dive into detail and share all my experience based on my experience all the basically how we design adaptive controllers learning algorithms what do we mean by learning adaptation it at first place and you will have a deep understanding of adaptive control theory and learning and if you have any issues about vectors and matrices well I strongly recommend that you also watch these videos Vector operations and Mathematics operations I am always honest with you well these videos you you may think you know watching them it is just abstract mathematics vector and Matrix operations it may be a bit boring but in the long term if you know of them this will be very important for your knowledge and understanding not only adaptive control lectures but also any other Advanced controls material so um once again I am happy to kick off this NIV lecture series on adaptive control and learning stay tuned new videos will come thanks for watching the very first video