Suboptimal control law for a near-space hypersonic vehicle based on Koopman operator and algebraic Riccati equation

This paper presents a novel suboptimal attitude tracking controller based on the algebraic Riccati equation for a near-space hypersonic vehicle (NSHV). Since the NSHV’s attitude dynamics is complexly nonlinear, it is hard to directly construct an appropriate algebraic Riccati equation. We design the construction based on the Chebyshev series and the Koopman operator theory, which includes three steps. First, the Chebyshev series are considered to transform the error dynamics of the NSHV’s attitude into a polynomial system. Second, the Koopman operator is used to obtain a series of high-dimensional linear dynamics to approximate each of the polynomial system’s vector fields. In this step, our contribution is to determine a well-posed linear dynamics with the minimal dimension to approximate the original nonlinear vector field, which helps to design the control law and analyze the control performance. Third, based on the high-dimensional dynamics, the NSHV’s attitude error dynamics is separated into the linear part and the nonlinear part, such that the algebraic Riccati equation can be constructed according to the linear part. Then, the suboptimal error feedback control law is derived from the algebraic Riccati equation. The closed-loop control system is proved to be locally exponentially stable. Finally, the numerical simulation demonstrates the effectiveness of the suboptimal control law.

Nonlinear suboptimal attitude control law for near-space hypersonic vehicle: Eigenvalue analysis and weight matrices design

This paper considers a nonlinear suboptimal control problem for a near-space hypersonic vehicle's (NSHV's) attitude dynamics. The least-square and stable manifold methods first solve an unconstrained approximately optimal control law corresponding to the nonlinear attitude model. Then, to further meet the dynamic performance requirement of the attitude control system, a novel strategy based on the Koopman operator, symplectic geometric theory, and the stable manifold theorem is proposed to approximate the eigenvalues of the closed-loop nonlinear unconstrained approximated optimal control system. The weight matrices in the optimal performance index, which directly determine the output responses of the nonlinear attitude dynamics, can be appropriately designed according to the eigenvalues. The final control law considers the actuator constraints. The NSHV's closed-loop attitude control system is proved to be locally exponentially stable, and the suboptimality of the control law is analyzed. Numerical simulation demonstrates the effectiveness of the proposed scheme.

Nonlinear suboptimal attitude control law for near-space hypersonic vehicle: Eigenvalue analysis and weight matrices design

This paper considers a nonlinear suboptimal control problem for a near-space hypersonic vehicle's (NSHV's) attitude dynamics. The least-square and stable manifold methods first solve an unconstrained approximately optimal control law corresponding to the nonlinear attitude model. Then, to further meet the dynamic performance requirement of the attitude control system, a novel strategy based on the Koopman operator, symplectic geometric theory, and the stable manifold theorem is proposed to approximate the eigenvalues of the closed-loop nonlinear unconstrained approximated optimal control system. The weight matrices in the optimal performance index, which directly determine the output responses of the nonlinear attitude dynamics, can be appropriately designed according to the eigenvalues. The final control law considers the actuator constraints. The NSHV's closed-loop attitude control system is proved to be locally exponentially stable, and the suboptimality of the control law is analyzed. Numerical simulation demonstrates the effectiveness of the proposed scheme.

SINS/BDS Tightly-Coupled Integrated Navigation Algorithm for Hypersonic Vehicle

A tightly-coupled integrated navigation system (TCINS) for hypersonic vehicles is proposed when the satellite signals are disturbed. Firstly, the architecture of the integrated navigation system for the hypersonic vehicle is introduced. This system applies fiber SINS, BeiDou satellite receiver (BDS) and SOPC missile-born computer. Subsequently, the SINS mechanization for hypersonic vehicle is presented. The J2 model is employed for the normal gravity of the near space. An algorithm for updating the attitude, velocity and position is designed. State equations and measurement equations of SINS/BDS tightly-coupled integrated navigation for hypersonic vehicle are given, and a scheme of validity for satellite data is designed. Finally, the SINS/BDS tightly-coupled vehicle field tests and hardware-in-the-loop (HWIL) simulation tests are carried out. The vehicle field test and HWIL simulation results show that the heading angle error of tightly-coupled integrated navigation is within 0.2°, the pitch and roll angle errors are within 0.05°, the maximum velocity error is 0.3m/s, and the maximum position error is 10m.

The thickness of the ventral medial prefrontal cortex (vmPFC) predicts the self-prioritization effect (SPE) on the interaction between spatial reference frames and spatial domains

Neuropsychological studies have demonstrated that the preferential processing of near-space and egocentric representation is associated with the self-prioritization effect (SPE). However, relatively little is known concerning whether the SPE is superior to the representation of egocentric frames or near-space processing in the interaction between spatial reference frames and spatial domains. The present study adopted the variant of the shape-label matching task (i.e., color-label) to establish an SPE, combined with a spatial reference frame judgment task, to examine how the SPE leads to preferential processing of near-space or egocentric representations. Surface-based morphometry analysis was also adopted to extract the cortical thickness of the ventral medial prefrontal cortex (vmPFC) to examine whether it could predict differences in the SPE at the behavioral level. The results showed a significant SPE, manifested as the response of self-associated color being faster than that of stranger-associated color. Additionally, the SPE showed a preference for near-space processing, followed by egocentric representation. More importantly, the thickness of the vmPFC could predict the difference in the SPE on reference frames, particularly in the left frontal pole cortex and bilateral rostral anterior cingulate cortex. These findings indicated that the SPE showed a prior entry effect for information at the spatial level relative to the reference frame level, providing evidence to support the structural significance of the self-processing region. The present study also further clarified the priority in SPE processing and role of the SPE within the real spatial domain.