Exponential sliding mode tracking control via back-stepping approach for a hypersonic vehicle with mismatched uncertainty

This paper develops the exponential sliding mode controller for a hypersonic vehicle to deal with the mismatched uncertainties via a back-stepping procedure. The dynamic equations in the longitudinal direction are first partitioned into two sub-systems of equations, one for velocity and the other for altitude. The mismatched uncertainties are prescribed by bounded functions. Then, following the back-stepping procedure the Lyapunov functions for these two sub-systems are constructed step by step and the exponential sliding mode control laws are formulated such that the control system can track the command input and reach steady state along the designed sliding surface. Meanwhile, the chattering phenomenon is eliminated. Theoretical proofs of these controllers׳ tracking performance and stability are presented. Simulations are conducted and the numerical results demonstrate that proposed controllers have good robustness to mismatched uncertainties, thus show good performance in the tracking of the desired reference signals.