# additional_exercises_sol_54.xlsx - You will carry out this...

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You will carry out this method for the following proble minimum or a weak minimum. You can generate the you to come to your conclusion. You can pick e = O.O set of 1% suboptimal points. The problem is a minimum fuel optimal control probl at time kh is given by p(k) G R 2 , and the velocity by the sampling period. These are related by the equati p{k + 1) = p(y + ( + 1) = (1 — a)0 o ) + O/m)f where /(fc) G R 2 is the force applied to the vehicle at a e (0,1) models drag on the vehicle; in the absense by the factor 1 — ce in each discretized time interva accurate formulas that i+olve matrix expo+eatials.) The force comes from two thrusters, and from gravit J(k) = . zj Ui(fc) + . Q U2(k) + , fc = 1, . . ' sint^i ' ' sm O2 —mg Here Ui(fc) G R and U2(fc) 6 R are the (nonnegative) directions of the thrust forces, and p = 10 is the con The total fuel use is K-l F £ ( ( + ( )• k=l (Recall that ui(fc) > 0, U2(fc) > 0.) The problem is to minimize fuel use subject to the in way-point constraints (k )~ 5 i = 1,..., AT".
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