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The problem of optimal thrust and path angle control is considered in the paper for given trajectory trajectories in the vertical plane when specific energy or altitude derivative with respect to time is not equal to zero. The minimized functional is assumed to be a fuel consumption. The range and endurance may be arbitrary or given. The path angle is not considered as a small value irrespective of using the energy approach. The problem is solved by means of the maximum principle. As a result the adaptive extreme control laws for aircraft thrust or path angle that provide the minimum fuel consumption have been obtained. These control laws have the form of ordinary differential equations. They may be used in simplification of some optimization problems and for the on-board implementation as regulators. The paper presents the results of calculations made for comparison of effectiveness of the proposed adaptive extreme control laws with the optimal solutions obtained from a sufficiently precise second order method. A difference in the relative fuel consumption is of an order of 0.02 -2 % for different examples.
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