Vehicle Control $($Continued$)$

$1/2$ points $($graded$)$

We can choose different criteria to define what is an $$optimal$"$ policy $,$ and result in different optimal control problems:

$1.$ Minimize the fuel consumption with given transition time :

Choose all the functions in the following such that they may serve as an objective function to minimize fuel consumption:

$.$

for some $.$

$.$

$.$

None of the above.

correct

$2.$ Given the maximum traction force $,$ i$.$e$.,$ for all $,$ consider minimizing the total time we need to achieve the goal:

Given the transition time $,$ e$.$g$.,$ we may be interested in monitoring the system for $100$ time steps. What is a good choice for the function to minimize the total time to achieve our goal?