My name is Enrique Zua Zua. I am the chair professor in Erlangen University, in Friedrich

Alexander University in Erlangen, close to Nuremberg in Bayern, Bavaria in Germany. I'm

also a part-time professor in Autónoma de Madrid and DEUSTO in Bilbao. I am actually

now in Madrid, in my home university, Universidad Autónoma de Madrid. And then two years ago,

we were founded by the Alexander Bochumbo Professorship to run a chair in Germany,

in FAO, in Friedrichs Alexander Universität. And this is where I am running most of my activity.

You have here the webpage of the chair, where you will find plenty of contents of the work

that we are doing. And as you will see, we are somehow driven by the two main forces, right?

On one side, we try to develop mathematics, computational mathematics methods. We have

mathematical functions, and this is what we like doing. But it's always good to get inspired on

some concrete applications like material sciences, traffic, biological models, multi-agent systems,

partial differential equations, inverse problems. So we try to cover a multifold agenda in which

we can integrate especially young people, either for master thesis, for PhD thesis, or for

postdoctoral training. So we try to integrate people with different, say, diverse interests,

so that they can meet together, they can work together, and in this way generate some kind of

dynamics of cross-fertilization. Okay, so this being said, you will find a lot of contents

in the webpage of our chair. I will show you maybe during the course over webpages as well.

Let me begin by telling you something about control. So in fact, it will be endless, right,

to indicate how many important applications to technology, to engineering, to economics,

to society control theory has. But just to give you a quick idea, this slide has been composed by

my friend Emmanuel Trela in Paris. There is of course a lot of applications to mechanics.

So mechanics you see here, aeronautics you see, astronautics you see, you know, the classical

pendulite, right, you see motion, this could be, you know, automobile, a car, right. There are more

and more applications of course also to biology, right, where biology as you know, biology,

medicine, biomedicine, biomedicine, modern techniques in medicine are meeting robotics,

so to make things, you know, operations to be sometimes realized by machines, by driven by

expert humans that oftentimes are not even on site so that they can guide, you know, remote

operations. Of course, electronics, electricity, energy, networks, gas networks, water networks,

irrigation, chemistry, of course chemical processes, every chemical product in order to be

well designed needs to follow a very specific dynamics that needs to be tuned, regulated,

controlled during the whole, say, time horizon and of course economics, right. So we know also

how important economics is. You can work very hard, I mean if the economy of your country is not

stable, all these efforts risk to dissipate a lot. So these are just a few mechanics, biomedicine,

electricity, energy, economics, chemistry, just some examples of very important fields in our lives

in which as soon as you will start, you know, checking how the most relevant processes are

working, you will find plenty of elements of control theory, control systems, dynamical

systems under control, right, optimization processes and precisely the lectures we are

delivering these days will be devoted to present some of the mathematical techniques that can be

employed in order to tackle these issues, right. Now in my previous slide I have indicated

some quite recent applications, right, contemporary applications, but actually the field of

control theory goes back to the very early, you know, civilization, right. So it was already

Aristotle, right, in his traditional book, Politics, who said something like this, he said

if every instrument could accomplish its own work obeying or anticipating the will of others,

if the shuttle waved and peak touched the line without a hand to guide them,

chief warmen will not need servant nor master's slave. So it was already 2500 years ago

that Aristotle is out of his mind just by through philosophical reflection that he realized

that in order to make the humans free, right, so to be, you know, so that they will be allowed

to be dedicated what they really like to do, playing music, doing a sport, doing mathematics,

whatever you like to do, cooking, walking, talking to your friends, in order to make humans free,

humans should be able to develop machines that will obey the will of humans and realize the task