bv_cvxbook_extra_exercises

A explain how to nd the optimal grading plan b find

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Unformatted text preview: 1 = (1 − η )vt + h(ft − bt ), t = 0, 1, . . . , where η ∈ (0, 1) is a friction or drag parameter, ft is the engine thrust, and bt is the braking force, at time period t. These must satisfy 0 ≤ bt ≤ min{B max , ft }, 0 ≤ ft ≤ F max , 122 t = 0, 1, . . . , as well as a constraint on how fast the engine thrust can be changed, |ft+1 − ft | ≤ S, t = 0, 1, . . . . Here B max , F max , and S are given parameters. The initial thrust is f0 = 0. The take-oﬀ time is T to = min{t | vt ≥ V to }, where V to is a given take-oﬀ velocity. The take-oﬀ position is P to = pT to , the position of the aircraft at the take-oﬀ time. The length of the runway is L &gt; 0, so we must have P to ≤ L. (a) Explain how to ﬁnd the thrust and braking proﬁles that minimize the take-oﬀ time T to , respecting all constraints. Your solution can involve solving more than one convex problem, if necessary. (b) Solve the quickest take-oﬀ problem with data h = 1, η = 0.05, B max = 0.5, F max...
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