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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). Problem (Q) is a minimax problem: the objective is to minimize the maximum value achieved along the interval of integration by some function of the variables of the problem. Problem (Q) is a nonclassical problem of the calculus of variations, in that it is not a particular case of the Bolza problem. It is called the Chebyshev problem. It must be noted that Chebyshev-type problems occur frequently in various branches of engineering.

Liniger and C. A. Willoughby, Efficient integration methods for stiff systems of ordinary differential equations, SIAM, 1. Numer. Anal. 7, 1 (1970). B. L. Ehle and J. D. Lawson, Generalized Runge Kutta processes for stiff initial value problems, 1. Inst. Math. Appl. 16, 11 (1975). J. D. Ramshaw, Partial chemical equilibrium in fluid dynamics, Phys. Fluids 23, 675 (1980). 2 Minimax Optimal Control and Its Application to the Reentry of a Space Glider A. MIELE AND P. VENKATARAMAN ABSTRACT. A transformation technique is employed in order to convert minimax problems of optimal control (also called Chebyshev problems) into Mayer-Bolza problems of the calculus of variations.

EQUATIONS OF MOTION In this section, we consider the reentry of a space glider whose trajectory is controlled by means of the angle of attack a and the angle of bank u. The following hypotheses are made: (i) the space glider is a particle of constant mass; (ii) the Earth is spherical and nonrotating; (iii) the acceleration of gravity g is assumed constant, g = go; (iv) the altitude above sea level h is negligible by comparison with the radius of the Earth ro; (v) the path inclination I' is sufficiently small, so that the approximations sin I' == 1', cos I' == 1 hold; (vi) the drag D and the lift L have the form D = D(h, V, a), L = L(h, V, a), where V is the velocity.

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Boeing 707 & Awacs In Detail & Scale by Alwyn T. Lloyd

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