Fractional-Order Sliding Mode Control of Air-Breathing Hypersonic Vehicles Based on Linear-Quadratic Regulator

Abstract

A new fractional-order sliding mode control (FOSMC) scheme is investigated for air-breathing hypersonic vehicles (AHVs). The control scheme proposed is designed based on linear-quadratic optimal theory. First, by using the technique of input/output feedback linearization, the longitudinal model of AHVs is linearized to be decoupled tracking-error dynamics. Second, a linear-quadratic regulator (LQR) is designed to ensure that the tracking-error dynamics converge to the equilibrium point as soon as possible. Based on LQR, a novel fractional-order sliding manifold is introduced. Subsequently, the FOSMC is designed to reject system uncertainties and reduce the magnitude of control chattering. Then, Lyapunov stability theory is used to prove the finite-time convergence of the closed-loop system. The simulations indicate that the proposed control scheme shows excellent performance and robustness in the absence of uncertainties. Compared with conventional integer-order sliding mode control (IOSMC), the high-frequency chattering of control input is drastically depressed.