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This paper proposes a novel strategy to design a suboptimal attitude tracking control law for a near-space hypersonic vehicle (NSHV) based on the Koopman operator and stable manifold theory. The nonlinear vector field of the NSHV attitude model is locally Lipschitz continuous and can be approximated by a high-dimensional linear system over a compact set. Linear and nonlinear parts of the attitude dynamics are determined based on this system. Subsequently, the stable manifold theory is applied to determine the unconstrained approximated optimal control law that is used to further consider the control input constraints of the NSHV attitude model. The suboptimality of the control law is analyzed, and the local exponential stability of the closed-loop system with input constraints is proven. Furthermore, the eigenvalues for the closed-loop nonlinear attitude error dynamics are analyzed. After the control input saturation, the nonlinear closed-loop error dynamics of the NSHV can be approximated by a high-dimensional linear system with a minimal dimension. The eigenvalues of this linear system indicate the stability and time response characteristics of the attitude error dynamics of the NSHV. The numerical simulation results demonstrate the effectiveness and suboptimality of the proposed attitude tracking control law and workflow of the eigenvalue analysis. [ABSTRACT FROM AUTHOR]

This article deals with the problem of attitude tracking control for flexible satellite under flexible vibration disturbance, actuator fault and time delay. Based on disturbance observer and fault tolerant control techniques, the flexible vibration disturbance and actuator fault are effectively estimated by disturbance observer and fault estimation observer, respectively. Meanwhile, a delay-dependent attitude tracking feedback controller is designed to ensure that the reference attitude is stably tracked. To reduce the conservatism of the designed algorithm, a time delay correlative decomposition factor is introduced to make the flexible satellite have a better performance for attitude tracking control. Finally, the effectiveness of the proposed method is illustrated by numerical simulations. [ABSTRACT FROM AUTHOR]