Problems associated with onboard trajectory optimization, propulsion system cycle selection, and the synthesis of guidance laws are addressed for ascent to low Earth orbit of an airbreathing, single-stage-to-orbit vehicle. A multicycle propulsion system is assumed that incorporates turbojet, ramjet, scramjet, and rocket engines. An energy state approximation is applied to a singularly perturbed, four-state dynamic model for flight of a point mass over a spherical nonrotating Earth. An algorithm is then derived for generating both the fuel-optimal climb profile and the guidance commands required to follow that profile. In particular, analytic switching conditions are derived that, under appropriate assumptions, efficiently govern optimal transition from one propulsion cycle to another. The algorithm proves to be computationally efficient and suitable for real-time implementation. It will accommodate general functional dependence on angle of attack, a normal component of thrust, acceleration limits, and constraints on maximum dynamic pressure and maximum aerodynamic heating rate. The paper concludes with the presentation of representative numerical results that illustrate the nature of the fuel-optimal climb paths and the tracking performance of the guidance algorithm.
