The fuel optimal control problem of a hypersonic aircraft with periodic cruising mode

In this paper, based on the periodic up and down cruising mode a controller design method for a hypersonic aircraft is addressed to achieve further voyage with fixed fuel by solving for ignition time of combined engine, throttle opening and the elevator deflection angle. A fuel optimal control problem of switched system is formulated, in which, ignition time, throttle opening and the elevator deflection angle are decision variables. The maximum principle is applied to find the throttle opening. Furthermore, the control parameterization method and the time scaling transformation are adjusted to transform the original optimal control problem into a normal nonlinear programming problem, which can be solved by the existing gradient-based method. Simulation results show the efficiency of the proposed method.