Disturbance observer based robust mixed H2/H∞ fuzzy tracking control for hypersonic vehicles

This paper introduces a disturbance observer (DO) based mixed H2/H∞ robust fuzzy tracking control design for the longitudinal dynamics of a generic hypersonic vehicle (HV) with modeled and unmodeled disturbances. A Takagi-Sugeno (T-S) fuzzy model is firstly employed to approximate the nonlinear dynamics of HV. Subsequently, based on the fuzzy model, a DO is constructed to estimate the modeled disturbance. Next, by integrating the HV dynamics, the tracking error integral and the disturbance estimation error dynamics, an augmented system is established for the control design. Then, a DO-based mixed H2/H∞ robust fuzzy control design is developed to ensure the asymptotic stability as well as the mixed H2/H∞ control performance of the augmented system. The proposed control scheme includes a fuzzy tracking controller with state feedback plus the tracking error integral, a robust nonlinear compensator for eliminating the matched part of the compound disturbance consisting of the unmodeled disturbance and fuzzy modeling error, and a DO-based compensator for the modeled disturbance cancellation. The outcome of the DO-based mixed H2/H∞ robust fuzzy control problem is formulated in terms of linear matrix inequalities (LMIs). Furthermore, by utilizing the existing LMI optimization technique, a suboptimal controller is obtained in the sense of minimizing an upper bound of H2 performance. Finally, simulation results on an HV demonstrate the effectiveness of the proposed design method.