Abstract
This article investigates the problem of guaranteed cost control for a flexible air-breathing hypersonic vehicle (FAHV). The FAHV includes intricate coupling between the engine and flight dynamics as well as complex interplay between flexible and rigid modes, which results in an intractable system for the control design. A longitudinal model is adopted for control design due to the complexity of the vehicle. First, for a highly nonlinear and coupled FAHV, a linearised model is established around the trim condition, which includes the state of altitude, velocity, angle of attack, pitch angle and pitch rate, etc. Secondly, by using the Lyapunov approach, performance analysis is carried out for the resulting closed-loop FAHV system, whose criterion with respect to guaranteed performance cost and poles assignment is expressed in the framework of linear matrix inequalities (LMIs). The established criterion exhibits a kind of decoupling between the Lyapunov positive-definite matrices to be determined and the FAHV system matrices, which is enabled by the introduction of additional slack matrix variables. Thirdly, a convex optimisation problem with LMI constraints is formulated for designing an admissible controller, which guarantees a prescribed performance cost with the simultaneous consideration of poles assignment for the resulting closed-loop system. Finally, some simulation results are provided to show that the guaranteed cost controller could assign the poles into the desired regional and achieve excellent reference altitude and velocity tracking performance.