Sliding Mode Differentiator Based Tracking Control of Uncertain Nonlinear Systems with Application to Hypersonic Flight

This paper presents a performance-guaranteed adaptive back-stepping design for a class of nonlinear systems with uncertainties and disturbances. To circumvent the increasing complexity caused by the repeated analytic differentiations in back-stepping, sliding mode differentiation technique is employed to estimate the derivative of the virtual control. Compared with the well-known command filtered back-stepping, no compensating signal is required. Besides, time-varying parameters, system uncertainties and external disturbances are compensated using nonlinear damping technique, while the output tracking error is regulated in the prescribed range with the adjustable convergence speed and steady-state error. As a verification example, this method is applied to the longitudinal control of an air-breathing hypersonic vehicle configured with the variable geometry inlet.