This paper is concerned with the near-optimum guidance of an aircraft from quasi-steady flight to quasi-steady flight in a windshear. The take-off problem is considered with reference to flight in a vertical plane. In...
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This paper is concerned with the near-optimum guidance of an aircraft from quasi-steady flight to quasi-steady flight in a windshear. The take-off problem is considered with reference to flight in a vertical plane. In addition to the horizontal shear, the presence of a downdraft is considered. It is assumed that the power setting is held at the maximum value and that the aircraft is controlled through the angle of attack. Inequality constraints are imposed on both the angle of attack and its time derivative.
This paper considers both classical and minimax problems of optimal control which arise in the study of aeroassisted, coplanar orbital transfer. The maneuver considered involves the coplanar transfer from a high plane...
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This paper considers both classical and minimax problems of optimal control which arise in the study of aeroassisted, coplanar orbital transfer. The maneuver considered involves the coplanar transfer from a high planetary orbit to a low planetary orbit. An example is the HEO-to-LEO transfer of a spacecraft, where HEO denotes high Earth orbit and LEO denotes low Earth orbit. In particular, HEO can be GEO, a geosynchronous Earth orbit.
This paper is concerned with guidance strategies for near-optimum performance in a windshear. This is a wind characterized by sharp change in intensity and direction over a relatively small region of space. The take-o...
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This paper is concerned with guidance strategies for near-optimum performance in a windshear. This is a wind characterized by sharp change in intensity and direction over a relatively small region of space. The take-off problem is considered with reference to flight in a vertical plane.
This paper is concerned with optimal flight trajectories in the presence of windshear. With particular reference to take-off, eight fundamental optimization problems [Problems (P1)–(P8)] are formulated under the assu...
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This paper is concerned with optimal flight trajectories in the presence of windshear. With particular reference to take-off, eight fundamental optimization problems [Problems (P1)–(P8)] are formulated under the assumptions that the power setting is held at the maximum value and that the airplane is controlled through the angle of attack.
This paper considers optimal control problems involving the minimization of a functional subject to differential constraints, terminal constraints, and a state inequality constraint. The state inequality constraint is...
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This paper considers optimal control problems involving the minimization of a functional subject to differential constraints, terminal constraints, and a state inequality constraint. The state inequality constraint is of a special type, namely, it is linear in some or all of the components of the state vector. A transformation technique is introduced, by means of which the inequality-constrained problem is converted into an equality-constrained problem involving differential constraints, terminal constraints, and a control equality constraint. The transformation technique takes advantage of the partial linearity of the state inequality constraint so as to yield a transformed problem characterized by a new state vector of minimal size. This concept is important computationally, in that the computer time per iteration increases with the square of the dimension of the state vector. In order to illustrate the advantages of the new transformation technique, several numerical examples are solved by means of the sequential gradient-restoration algorithm for optimal control problems involving nondifferential constraints. The examples show the substantial savings in computer time for convergence, which are associated with the new transformation technique.
This paper considers the numerical solution of optimal control problems involving a functional I subject to differential constraints, nondifferential constraints, and terminal constraints. The problem is to find the s...
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This paper considers the numerical solution of optimal control problems involving a functional I subject to differential constraints, nondifferential constraints, and terminal constraints. The problem is to find the state. x(t), the control u(t), and the parameter pi so that the functional is minimized, while the constraints are satisfied to a predetermined accuracy. The approach taken is a sequence of two-phase processes or cycles, composed of a gradient phase and a restoration phase. The gradient phase involves a single iteration and is designed to decrease the functional, While the constraints are satisfied to first order. The restoration phase involves one or several iterations and is designed to restore the constraints to a predetermined accuracy, while the norm of the variations of the control and the parameter is minimized. The principal property of the algorithm is that it produces a sequence of feasible suboptimal solutions: the functions x(t), u(t), pi obtained at the end of each cycle satisfy the constraints to a predetermined accuracy. Therefore, the functionals of any two elements of the sequence are comparable. The stepsize of the gradient phase is de: ermined by a one-dimensional search on the augmented functional J, and the stepsize of the restoration phase by a one-dimensional search on the constraint error P. If alpha(g) is the gradient stepsize and alpha(r) is the restoration stepsize, the gradient corrections are of O(alpha(x)) and the restoration corrections are of O(alpha(r)alpha(2)(g)). Therefore. for alpha(g) sufficiently small the restoration phase preserves the descent property of the gradient phase: the functional (I) over cap at the end of any complete gradient-restoration cycle is smaller than the functional I at the beginning of the cycle. To facilitate the numerical solution on digital computers, the actual time theta is replaced by the normalized time t, defined in such a way that the extremal arc has a normalized time length Delta t
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