Minimax LQR control design for a hypersonic flight vehicle

For the longitudinal motion of air breathing hypersonic vehicles (AHFVs), a minimax linear quadratic regulator (LQR) control is synthesized considering seven uncertain aerodynamic and inertial parameters. The minimax control strategy works under the assumption that the uncertainties satisfy certain integral quadratic constraints, and provides robust stability as well as robust performance for the AHFV system with uncertainties. The design utilizes the effectiveness of the widely used feedback linearization technique with a special treatment of the non-vanishing nonlinear terms in the presence of uncertainties. The outputs to be controlled are the longitudinal velocity and altitude, and the control variables are the throttle setting and elevator deflection. The performance of the controller is evaluated at a particular cruise condition at Mach 15 with 100ft/sec and 2000ft commands for velocity offset and altitude respectively. Results for the proposed controller are also compared with results in the literature utilizing adaptive sliding mode and stochastic robustness based controllers, and the proposed minimax controller is demonstrated to be more robust than these approaches in the presence of uncertainties.