AEROSPACE PLANE GUIDANCE USING TIME-SCALE DECOMPOSITION AND FEEDBACK LINEARIZATION

Single-stage vehicles using air-breathing propulsion hold promise for more economical delivery of payloads to orbit. Feedback guidance logic is developed for steering and accelerating such a vehicle along the super- and hypersonic segments of a near-minimum-fuel ascent trajectory. Accurate solutions of the minimum-fuel ascent problem show the effects of dynamic pressure, acceleration, and heating constraints and establish a basis for the development and assessment of guidance logic. The two-time-scale behavior in the optimal solution allows the state space to be decomposed into a control-dependent slow manifold and a family of fast manifolds. Near-optimal guidance is obtained by constructing a composite control law from the control for flying the minimum-fuel reduced-order trajectory on the slow manifold and a control for tracking the optimal reduced-order trajectory. The tracking problem is solved as a family of regulation problems corresponding to the family of fast manifolds, using the feedback linearization methodology from nonlinear geometric control theory. A complete characterization is given of all state transformation-static feedback pairs that lead to exact linearization of the fast dynamics. Simulation shows that the composite control law produces a near-minimum-fuel ascent.