A vehicle with unit mass has velocity v. A force u can be applied and a linear drag term acts on the vehicle, such that
Posted: Wed May 18, 2022 5:18 pm
- A Vehicle With Unit Mass Has Velocity V A Force U Can Be Applied And A Linear Drag Term Acts On The Vehicle Such That 1 (42.93 KiB) Viewed 58 times
A vehicle with unit mass has velocity v. A force u can be applied and a linear drag term acts on the vehicle, such that the vehicle dynamics is i(t) = u(t) – v(t). Initially the vehicle is at rest, i.e. v(0) = 0. The goal is to drive the vehicle to a final velocity of v(T) = 1. a) Suppose u(t) € (-0.1,0.1) for all t. Is the control problem feasible for any T > 02 Show why or why not. [4 points) b) Suppose u(t) € R for all t. Additionally we are to minimize the following cost: lutydt NI where T In(2). Solve for the input u(t) and state v(t) that minimize this cost using Pontryagin's Minimum Principle. (12 points) c) Suppose u(t) € (-ū, ū), ū= 1-20 for all t. Solve the time-optimal control problem, that is, solve for the end time T, input u(t) and state u(t) that minimize the cost " dt using Pontryagin's Minimum Principle. [13 points)