Thank you. At first, I would like to thank Tobias for the invitation. And I also want

to thank him for pronouncing correctly my Chinese name. So actually, so my name is sentientian.

And actually, I also get a French name. The French name is synchronous. So as you can

imagine the reason that I get relaxation. So yeah, thank you.

And this talk will be about control theory, more precisely

about stabilization of some PD models. And it's a joint

work, my courses, UTV, GAN, Mochi, Hi-hat, Crystal Zone, and

of course, Chumshui and Guohong. So this talk will be composed

by three parts. And the first part, I will briefly talk about

recall some basic definition about stabilization problem and

also control problems. And second part is about frequency

near proof that is a method that I introduced that can be used

to get finite time stabilization problems. And

finally, if time permits, I will introduce some recent

development in free frame backstabbing that corresponds to

rapid stabilization. So let's begin. The problem that we're

interested in is control theory. And this is a control problem.

Well, x is a state, u is the control. So controllability means

whatever gives you x0 and x1, can you construct control u such

that the unique solution starts at x0 and ends at x1. And that's

typical definition. And today, there's another topic that we

are focused on is called stabilization means that

whatever gives you unstable system, can you construct feedback

more to make the closed loop system stable? Explanationally

means the solution decays exponentially like exponential

stabilization. Here I just have a very simple example. For

example, if you look at this system, x dot equals x, you know

that the solution will increase so it's not stable. But on the

other hand, if I just add some control terms, so this is the

original term, if I add a control term, which looks like

this, and then it becomes minus x and it actually decrease. So

this process is stabilization. We can also have a look at this

simple example here. It's unstable system because if

imagine that if this man doesn't do anything, he may probably

fall down. However, with a stick on his hand and moving his

stick, he's able to keep balance and this balancing

procedure is stabilization. So typically, there are two kinds of

control. The first part is internal control where the

control x internally in a domain and boundary control as you can

see a free, so the free just pass through the boundary. This

is a boundary control and stabilization problem appear

everywhere. For example, the open channel of the river, we

want to stabilize the river and the traffic road problems. And

as you can see from this picture, if you don't stop in

light of the traffic, you can never imagine what would happen.

So this is actually come from the film, La La Land. Once you

cannot stabilize the traffic, people will probably start to

bounce. And this picture actually come from out of the

earth in the mass. So here this is also you see the gas here is

also stabilization mechanism. Sometimes we need a very fast