This preview shows page 1. Sign up to view the full content.
Unformatted text preview: 0.) The problem is to minimize fuel use subject to the initial condition p(1) = 0, v (1) = 0, and the
waypoint constraints
p(ki ) = wi , i = 1, . . . , M.
(These state that at the time hki , the vehicle must pass through the location wi ∈ R2 .) In addition,
we require that the vehicle should remain in a square operating region,
p( k ) ∞ ≤ P max , k = 1, . . . , K. Both parts of this problem concern the speciﬁc problem instance with data given in thrusters_data.m.
(a) Find an optimal trajectory, and the associated minimum fuel use p⋆ . Plot the trajectory p(k )
in R2 (i.e., in the p1 , p2 plane). Verify that it passes through the waypoints. 19 (b) Generate several 1% suboptimal trajectories using the general method described above, and
plot the associated trajectories in R2 . Would you say this problem has a strong minimum, or
a weak minimum?
3.17 Minimum fuel optimal control. Solve the minimum fuel optimal control problem described in
exercise 4.16 of Convex Optimization, for the instance with problem data −1 0.4 0.8 0
0 ,
A= 1
0
1
0 1 b = 0 ,
0.3 xdes 7 = 2 ,...
View Full
Document
 Fall '13
 F.Borrelli
 The Aeneid

Click to edit the document details