With this broad definition of a cyber-physical system, one might like to wonder what kind of systems fit into this class of systems and what class of systems were interested in this course. So I would like to summarize this by generating a diagram that in the center we have cyber-physical systems. The acronym of cyber-physical systems is CPS, and I would like to draw a specific class of applications I know, basic tools or methods that we will like to understand as part of this course, but that actually makes cyber-physical systems very interesting and relevant field of study. So on the top right, I would like to write down robotic systems. Robotic systems are a wide class of systems. You can think about robotic manipulators, you can think walking robots, you can think of any type of autonomous system, and this class of system has very clear physical components. And the cyber part in addition to the interfaces that play the most key part on the system is the algorithm that tears the rubout in particular directions. Another specific class is multiple vehicular systems. These are systems that are perhaps, semi-autonomous. They involve humans and they involve algorithms. And the fact that there are multiple, you could probably relate to autonomous sort of self-driving cars that you probably experience every day without autonomy, but you would probably agree with me that the future shows that cars will have a lot of autonomy over the next few years. And these systems, each car will have their own physical description and then they will have a network that will allow them to communicate. And now algorithms that will permit safe navigation and perhaps, optimal navigation in the roads. Another area where cyber-physical systems are very prevalent is power networks, and we use these daily even though we sometimes do not realize. When we use our power at home or at the office, where we power our devices. The trend is that these power will actually be self-generated using renewable energy or different locations and they will be a network that would allow us to share the power and decide which source should be use at a given time. The physics here are very interesting. You have the electronics, the circuitry that corresponds to the conditioning and transfer of power over power system, our electrical system and also you have algorithms for communication and control. So all these different application areas are areas of interest and relevance to cyber-physical systems. There are many others, but these are the ones that we find most interesting at this stage. Now when we talk about how to analyze or synthesize controllers on interfaces for a cyber-physical system, we naturally come to the field of digital communication and control. Digital communication is natural and allow us to do communication with security and also wirelessly and with a somewhat simple way to interface to computers as most of you might agree with me. The part of control which is digital is because most of the control algorithm these days are implemented on computer. It could be very small computers like just microcontrollers or very large computers. And those implementations of a control algorithms are typically done using some code. That code is the part of this cyber that we will like to understand in this course. The other portion that I have prepared to discuss over this course is advance control and because of the nature and complexity of our cyber-physical system, one is interested in understanding logic-based algorithms. The point is that this cyber-physical system is something so complex that you need to somehow partition the space of the system and use different strategies in different regions of the state space or the space of operation will define what a state space means soon. But the idea is that you have a logic system that will supervise different algorithms and each algorithm may be designed using different tools. May be used in digital control techniques. And when we get to the point of particular feedback or making decisions with information that we have available, we unavoidable enter a problem which is that we don't have all the information available all the time. So, one of the key techniques that we will need in order to understand cyber physical systems and synthesize them is how to estimate with limited information, the variables of the system. Now, I referred the system again as a cyber-physical system. So we might want to estimate not only the position and velocity of my robotic system or my vehicle or the current and the voltage of the power network, but maybe also the variables inside the control algorithm that we're actually implementing, and we might not have access all the time because of different processor requirements or loads. So these are the type of tools that we'll be focusing and our key to cyber-physical systems, but on the other side, these are the key driving applications for this field in this course. One thing that I would like to mention here is a similarity with embedded systems. Embedded systems have been around for many, many years. Cyber-physical systems are similar to embedded systems, but the big difference is that the environment which is what is part of an embedded system, in our case, are the physics. And those physics play a key role, and they actually changed the way we need to design the cyber part. So as I said in the previous slide, typically, we cannot design the physics and the cyber separately as done in embedded systems. We actually really want to make sure that the environment is handle the right way.
