Ascent Phase Trajectory Optimization for a Hypersonic Vehicle Using Nonlinear Programming

In this paper we present a nonlinear programming solution to one of the most challenging problems in trajectory optimization. Unlike most aerospace trajectory optimization problems the ascent phase of a hypersonic vehicle has to undergo large changes in altitude and associated aerodynamic conditions. As a result, its aerodynamic characteristics, as well as its propulsion parameters, undergo drastic changes. Further, the data available through wind tunnel tests are not always smooth. The challenge in solving such problems lies both in the preprocessing of the data as well as in the judicious use of optimization techniques. In this paper we advocate approximation of the infinite dimensional optimal control problem, derived from practical considerations of a hypersonic vehicle ascending from an altitude of 16 kms to an altitude of 32 kms with specified mach numbers, into a set of finite dimensional nonlinear programming problems. This finite dimensional approximation is shown to produce acceptable optimized results in terms of angle-of-attack control histories and state behaviour. A modification, that exploits the ultimate scheme of linear interpolation of the optimal discrete history, is proposed and is shown to produce accurate results with smaller number of grid points.