[MOVED] Model Predictive Control Basics

Hi,
I am learning basics about Model Predictive Control and have a few doubts which I don't find addressed anywhere

1)If the control horizon is lesser than predicted horizon,how is the output plotted for those points where there is no control input (i.e) beyond the control horizon?
2)What is the meaning of control cost?I found an article which states that the objective function for control cost is basically the square of amplitude of input control signal.Where did that come from?And why do we have to take the input signal into optimization?
3)Can the objective function for the various costs be anything?Or can we frame our own objective function which defines the performance of the system in the best way?

Thanks a lot for your response.

Q #1.
Since you do not want to leave a question mark in the space where you cannot predict outcome, it is more informative if you generate a few likely scenarios, and then plot actions you would take.

Q #2.
Drawing on electrical terminology... if you double the voltage, you quadruple the power. You must devise a control system that can handle four times the power.

Or it could also be like saying that if you wait 2x as long to take action, you must spend 4x as much (energy, money) as if you'd done it sooner.

Q #3
We gain valuable information when we examine ideal scenarios, even ones that are impractical. Doing so helps us to find a median between various tradeoffs, as to performance, cost, availability, etc.

We ought to 'think outside the box.' By doing so we might discover some way to improve the system.