With the model of the physics given by differential equations and of the cyber given by difference equation, what we would like to understand now is how to interconnect these systems. I mean, we think about how the interconnection occurs in the cyber physical system itself in the hardware. What we typically have is the physics and the cyber connected through some interfaces. You can think about these interfaces as single conditioners, converters, or even networks. The interfaces will allow the signals that the physics generates to be compatible with the signals that the cyber requires on the other way around. So you can think of having a closed loop system where information flows in this direction, but different interconnections might be possible based on the application of interest. Now, we already know that one possible and powerful way to model the physical components is using differential equations with constraints. The constraints will potentially be on the state. Remember Z or in the input U. A similar type of model can be used for the cyber. But now, it will be based on difference equations, because the natural behavior in this component is discrete. For the interfaces, because they do these translation of the signals, we might expect that we will have models that involve the two type of objects, differential equations and difference equations. So there is some sort of partition here on the dynamics. So we are going to believe for a second that this combined differential and difference equations of course with potential constraints, and with these models, we can actually have our events triggered by state and inputs of each of the systems where the inputs now for these interfaces will be the outputs of the components that we will describe. For the interfaces themselves, we're going to touch on a few of these. The first one that we're going to work on will be one that will be useful to convert analog signals into digital signals and would be useful to motivate the idea of modern interfaces in general. This will be an analog to digital converter, ADC for short, and then digital to analog converter, DAC. And then, using the ideas to model these two, we will arrive to a digital network model. When I mention key events, if you consider these converter, you could envision that every time that the signal here, a sample, and convert it into digital number, that is an event. So we have here conversion events and the same here. On the other hand, in the network model where we will have our communication events. The idea for us will be to come up with models of each of these that we're going to do in the forthcoming videos. And then, once we have those models, we can come up with a full CPS model that uses the models that we already know for the physics. And if you use a finite state machine or if you use a discrete algorithm, we know that already. And then within your model that we are about to derive, we will be able to actually build that big model which will involve necessarily differential equations, difference equations, and these events that we're talking about.
