For Question 1, a negative-feedback controller like a thermostat works by measuring the difference between the actual state x of the system and the desired state x-hat of the system
If the quantity x minus x-hat is negative, it turns down the heat
And this is false
This would be a positive feedback controller
If we just put in some numbers for x and x-hat, this will make this obvious
Consider the setpoint where we want our room to be 21 °C
Then x-hat would be 21
Say the room was actually 20 °C
So the room was colder than we wanted it to be
Then 20 21 is a negative quantity, and this would turn down the heat
So if the room was 20 °C, and we wanted it to be 21 °C, then we would turn down the heat, making the room even colder
This is known as positive feedback
What were asked about in this question, however, is negative feedback
So this question is false
For Question 2, OGY controls can be used to balance a chaotic system on one of its unstable periodic orbits, and this is true
This is one of the major applications of OGY control
Question 3 states that the denseness with which any trajectory in the basin covers a chaotic attractor plays a critical role in OGY control, and this is also true
The denseness with which any trajectory in the basin covers a chaotic attractor is how you get to any unstable periodic orbit
This allows you to get very close to or within one of those boxes like in the video of an unstable periodic orbit
So this question is also true