Data-Driven Control with Machine Learning – Part 1

So recently I have been interested in this new fascinated topic: data-driven control with machine learning. I accidentally discovered this topic when I was studying control theory for my course, dynamics and controls of space structures. Since this course requires me to understand control theory as its prerequiste, I had a hard time finding and learning the right materials to catch up quickly the topic, and I stumbled upon a youtube channel of Steve Brunton. He is a professor in mechanical engineering at University of Washington. He has a youtube channel which contains his free lectures about mathematics and engineering. From his channel I learn a lot about control theory, and he also hosts a very fascinating lecture series about data-driven control with machine learning. So in this post and for the upcoming posts, I am going to be talking about data-driven control which I learn from his lectures in brief way, and this is the first part

So, let’s first start with control theory. Basically, in control theory we want to manipulate a particular system dynamics with a controller so it achieves desired goals. The scheme is depicted as follows.

Schematic representation of dynamical system and its control (source: Machine Learning Control –Taming Nonlinear Dynamics and Turbulence)

We have physical system which is disturbed by some disturbances, and we want this system to behave like we want, and we measure this behaviour by introducing cost function (hence our goal is to minimize this cost function). To achieve this, we introduce control law which produces prescribed control through actuators to steer the dynamics, and hence this control law needs input (which is given by sensors obviously). So the problem with classical and modern control theory are (classical: one with frequency domain analysis, modern: one with time domain, state space, and siso-mimo):

  1. Highly non-linear dynamics: oftentimes, the dynamics we want to control are highly nonlinear, for example we want to laminarize the turbulent flow over the wing using flap (hence lower the drag and increase the lift). Classical and modern control theory relies on linearization of system dynamics. By having linearized system dynamics, we can easily construct cost function, hence by using various control law, such as kalman filter, LQR, or optimal control, we can easily control this dynamics. But, what if our system is highly non-linear, like the case I mentioned before? Then the cost function would be very complicated and cannot be solve using existing control law (remember Riccatti’s equation, right). So this problem needs a new approach.
  2. Unkown dynamics:
  3. Very high multidimensional parameter:
  4. Limited measurements:

What is control? what is machine learning?

  1. Data driven model
  2. Learn control
  3. Sensors/actuators placement

Exams in Polimi

Well guys, it has been a while I don’t write any post, and now I am back lol. So I have been so bussy with all exams, which is quite a nightmare. Well yeah, this is the type of exams I have never faced them before. OK, in this post, I would like to share my experience and opinion about exams in polimi (but it’s based on exam in my program which is Master in Space Engineering).

Okay, let’s start with the easiest one. And it’s technical communication in english. Literally there’s no exam in this course. All we have to do is just form a group consists of 8 to 10 people, then choose a topic to discuss, and at the end of the semester we have to present our work to the professor. As long as we present our work before the exam date, we might pass this course, so nothing special.

Now the 2nd course is Heat Transfer and Thermal analysis. This course is almost exactly the same as the heat transfer course which I took during my undergrad study in ITB, but this time the exam is MUCH MUCH harder. Why? Because the exam has something like ‘threshold’ system I would say. So the exam consists of two parts, part A and part B. Part A is 7 questions of multiple choice, and part B is essay with 3 questions. Part A acts as a threshold: the terrifying part is, if we only have less than 5 points from part A, then the part B will not be evaluated at all, and this means an instant failure. If we only have 5 points of part A, then part B will be evaluated and the score will be reduced by 3. If we have 6 correct from part A, then part B will be evaluated and there’s no reduction nor addition to the score of part B. And if we get 7 correct out of 7 from part A, then we will have bonus of 3 points added to the score of part B. This threshold system makes many students fail to pass the exam. I happened to pass the exam, and I was so lucky. But overall the failure rate is up to 40-50%! (during my exam, about 70 out of 170 students fail to pass minimum grade which is 18/30) Man, that was so insane. There’s no such high failure rate exam during my undergrad in ITB! And this kind of exam system actually puts a lot of pressure to the students, but, what can we do?

Third exam is Space Propulsion. This one actually quite easy, because we can obtain 20 points at max from the project alone, and another 12 points from the exam. But, again, there’s a threshold system here. IF we failed to obtain 6 points from the exam, then our points from the project will not be considered at ALL! And that really puts a lot of pressure to me, since the materials I have to study are so many. But alhamdulillah, I managed to obtain 6 points and I passed the exam. This exam also have quite low of failure rate, only about 20 students out of 200 failed this exam.

And here comes the most nightmarish exam among aerospace (both aeronautic and space) students: Dynamics and Control of Space Structures. This is bacuse the complexity of the mathematics and its plenty of prequisite knowledge. We have to at least understand well about: control, structure, vibration, and dynamics. Since during my undergrad I was not into those stuffs, I really put a lot of efforts for this exam alone. I studied 2 weeks straight 8-10 hours a day for this course ( well thats because I have to sharpen my knowledge about those prequistes). This time it does not have any threshold systems, but this time we have oral exam. At first, oral exam seems so frightening to me, but when I did the test, well that was actually not that bad. I managed to pass this exam with grade of 23 out of 30. I did a fundamental flaw during the exam and it made me to get only 23, but actually that was more than enough since I only wished to pass a mere 18, because I need to pass this course (regardless the score) in order to be eligible to the next year DSU scholarship (which made me have to pass 28 CFU in minimum before 10th August). And alhamdulillah, I managed to obtain 28 CFU today. That was really a lot of strugle. I have never done such insane thing before, such as studying 2 weeks straight without any break for 8-10 hours a day. I have to do this because this is the only way I can pass the courses. In ITB I never study that hard, actually ITB is quite easy to get high mark.

OK, thats all for today’s post. I hope I manage to write another post the other day. See ya later!

MSc in Space Engineering at Politecnico di Milano — Part 1

Hello everyone, today I would like to share my experience so far studying MSc in Space Engineering at Politecnico di Milano. It’s been almost 3 months of studying and the semester is about to finish, and so the exam is waiting. Actually due to coronavirus and national lockdown, I have not attended any physical classes at all because campus activities are also being closed, so the lectures all are delivered via online using Microsoft Teams. Therefore, the lecture experience is completely different if we compare with previous year before coronavirus outbreak.