Robust <formula formulatype="inline"><tex Notation="TeX">$L_{\bm \infty}$</tex></formula>-Gain Fuzzy Disturbance Observer-Based Control Design With Adaptive Bounding for a Hypersonic Vehicle

Abstract

A novel robust fuzzy disturbance observer-based control (DOBC) design methodology with adaptive bounding is proposed for the longitudinal dynamics of a generic hypersonic vehicle (HV) with modeled and unmodeled disturbances. A Takagi-Sugeno (T-S) fuzzy model is first employed to approximate the nonlinear dynamics of an HV. Subsequently, a new fuzzy disturbance observer is constructed to estimate the modeled disturbance. An augmented system with multiple disturbances is thus obtained by combining the dynamics of HV and the state estimation error of the modeled-disturbance generator. Then, a robust L∞ -gain fuzzy DOBC design with adaptive bounding is developed to guarantee that the closed-loop augmented system is semiglobally input-to-state practically stable (ISpS) with an L∞-gain performance. In the proposed control scheme, the compound disturbance, including the unmodeled disturbance and the approximation error in fuzzy modeling procedure, is divided into the matched part and the mismatched one, which are attenuated by adaptive bounding control and L∞ -gain control, respectively. The outcome of the robust L∞-gain fuzzy DOBC problem is formulated as a linear matrix inequality (LMI) problem. Moreover, by means of the existing LMI optimization technique, a suboptimal controller is obtained in the sense of minimizing an upper bound of L∞-gain, meanwhile a control constraint is respected. Finally, simulation results demonstrate the effectiveness of the proposed controller.