Constraints on time in Model predictive controller (MPC)?

Hello,

I am bit familiar with MPC and optimization routine by defining the cost function.

My question is, generally we see MPC has cost function (if we talk about linear MPC) of the form (see the picture attached.)

Is there any possibility to add or alter this cost function

For example, I am solving an optimal control problem where the time of arrival of vehicles at a particular location is also important. How can I change or modify this to include time as well in my optimization routine?.

Can anybody help me with this?