bv_cvxbook_extra_exercises

The relaxed solution xrlx can also be used to guess a

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Unformatted text preview: 0.) The problem is to minimize fuel use subject to the initial condition p(1) = 0, v (1) = 0, and the way-point 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 way-points. 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 ,...
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