A realtime approximate optimal guidance law for flight in a plane
Abstract
A realtime guidance scheme is presented for the problem of maximizing the payload into orbit subject to the equations of motion of a rocket over a nonrotating spherical earth. The flight is constrained to a path in the equatorial plane while reaching an orbital altitude at orbital injection speeds. The dynamics of the problem can be separated into primary and perturbation effects by a small parameter, epsilon, which is the ratio of the atmospheric scale height to the radius of the earth. The HamiltonJacobiBellman or dynamic programming equation is expanded in an asymptotic series where the zerothorder term (epsilon = 0) can be obtained in closed form. The neglected perturbation terms are included in the higherorder terms of the expansion, which are determined from the solution of firstorder linear partial differential equations requiring only integrations which are quadratures. The quadratures can be performed rapidly with emerging computer capability, so that realtime approximate optimization can be used to construct the launch guidance law. The application of this technique to flight in threedimensions is made apparent from the solution presented.
 Publication:

IN: 1990 American Control Conference
 Pub Date:
 1990
 Bibcode:
 1990amco....3.2356F
 Keywords:

 Optimal Control;
 Payload Delivery (Sts);
 Real Time Operation;
 Rocket Flight;
 Spacecraft Guidance;
 Aerodynamic Forces;
 Angle Of Attack;
 Partial Differential Equations;
 Space Communications, Spacecraft Communications, Command and Tracking