Finite-time Adaptive Control of Flexible Hypersonic Flight Vehicle under Measurement Noise

This paper investigates a finite-time composite adaptive control strategy for hypersonic vehicles under model uncertainties and measurement noise, employing state observers. To mitigate the impact of stochastic uncertainties and measurement noise, a nonlinear observer with exponential convergence characteristics is designed to filter noise and generate state estimates. As the observer gain increases, the stable attraction domain broadens, and the observation error's convergence time decreases. Considering the differing timescale characteristics of rigid body dynamics and flexible modes, singular perturbation theory is applied to perform fast-slow timescale decomposition. For the slow subsystem associated with the rigid body dynamics, dynamic uncertainties are addressed by deriving an aerodynamic parameter estimation update law, based on feedback from tracking errors and prediction errors. Both external tracking evaluation and internal estimation evaluation are integrated into the estimator to estimate the true values of aerodynamic parameters within a finite time, thus approximating dynamic uncertainties. For the fast subsystem corresponding to the flexible modes, an adaptive sliding mode controller is designed to stabilize the flexible dynamics. The exponential stability of the state observer, as well as the finite-time convergence of both the rigid and flexible modes, are analyzed using Lyapunov's direct method under simplified assumptions. Simulation results validate the observer-based controller's robustness against noise disturbances and its capability to accurately approximate uncertainties, resulting in enhanced tracking performance for speed and altitude.