Solutions manual to: Fundamentals of aerodynamics by John David Anderson

By John David Anderson

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Y) indirectly as follows: K i ,=b;(Y)·S,(Y)=b7(y)·s,(y) i=1,2, ... ,n, r=1,2, ... 1) Thus K, is completely determined. Instead of determining aim by looking solely at N iii (y) = 2: m=l i=1,2, ... 2) we imposed the requirement of the fast S';s as mentioned earlier. 16d)]. 6d), we have S; = S, - 2:" ii7 K" ;=1 S'; is null whenever S; is null. r=1,2, ... 1), we have r=1,2, ... 5) Hence, S;(y) is a null vector [and consequently S';(y) is nUll] if 2:" aimKi, = ;=1 8m" m=1,2, ... 3) must be respected by aim.

As a result of the transformation, the unknown minimax value of the performance index becomes a component of the vector parameter 1T being optimized. The transformation technique is then applied to the following Chebyshev problems of interest in the reentry of a space glider: (01) minimization of the peak dynamic pressure; and (02) minimization of the peak heating rate. Numerical results are obtained by means of the sequential gradientrestoration algorithm for solving optimal control problems on a digital computer.

8) ° 2. MINIMAX PROBLEMS Within the formulation represented by Problem (P), an important class of problems has been omitted. These problems occur when the minimization of the integral performance index (1) is replaced with the minimization of a local performance index having the following form: I = max F, t F = F(x, 7T', t), (6) Minimax Optimal Control 23 Thus, the following optimal control problem arises. PROBLEM (Q). Minimize the functional (6) with respect to the state x(t), the control u(t), and the parameter 71", which satisfy the constraints (2)-(5).

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