In this way, what we are going to write here would be to following model,

a final testing machine with cars,

where the output is now flipping on/off to one, zero.

And the transitions occur when

this function l is less or equal than zero.

These definitions are falling out of what we just describe.

So the transition function

will be given on or off.

It will give on if q

is off and it will be off if q is on.

This function will only be evaluated or executed whenever a transition occurs.

The function l, q, v,

theta will actually only open on q and v. What we would like to

have is that this function is less or equal than

zero when am in either this condition or in this condition.

So we can pick a negative number like minus one if this condition is true.

And T, which is the input in this case,

v is large or equal than T-max.

Or q is equal to off and v is less or equal than T-min.

Otherwise, we will have a positive number.

Another positive number could be just one.

For the output function,

all we need to do is to change on into

one in order to fit this system and generate a growth of the temperature

when q is equal to on or q from off to zero

to actually let the temperature decay according to the rate of decay, A.

So in this case, we are going to have a conversion between zero and one.

And this is just a static map that corresponds to the following function.

This defines a full CPS system.

It involves physics.

In this case, the temperature. It involves the cyber.

In this case, the logic that we

design in order to keep the temperature within these ranges.

And the full system has continuous dynamics here and by

the differential equation and discrete dynamics given by this discrete time system.

And if you were to simulate this,

which is something you're going to learn how to do soon,

you could probably envision trajectories of temperature that,

as a function of time,

if this is my value T-max and this is my value T-min, then the temperature,

if it starts at the value of a low T-min,

will grow all the way to the value of the threshold with q equal to on.

When that happens, it's going to start decaying.

When you reach the value T-min,

it will switch from off to on and this will continue over and over.