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Rigid spacecraft nonlinear robust \(H_\infty \) attitude controller design under actuator misalignments

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Abstract

\(H_\infty \) control is well-known for its robustness performance, but the spacecraft attitude \(H_\infty \) controller design under actuator misalignments and disturbances remains unexplored. In addition, the heavy computational demands prevent the implementation of an \(H_\infty \) controller for nonlinear systems in higher dimensions. To address these challenges, a robust \(H_\infty \) controller is proposed for the rigid spacecraft attitude control problem in the presence of actuator misalignments and disturbances based on the solution of the Hamilton–Jacobi–Isaacs (HJI) partial differential equation (PDE). The \(L_2\)-gain of the closed-loop system is proved to be bounded by a specified disturbance attenuation level. An efficient sparse successive Chebyshev–Galerkin method is also proposed to solve the nonlinear HJI PDE, thus the implementation of the proposed controller is facilitated. It is also proved that the computational cost grows only polynomially with the system dimension. The effectiveness of the proposed robust \(H_\infty \) controller is validated through numerical simulations.

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  1. Department of Navigation, Guidance, and Control, Northwestern Polytechnical University, Chang’an District, Xi’an, 710072, Shaanxi Province, People’s Republic of China

    Zhong Wang & Yan Li

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  1. Zhong Wang
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Contributions

All authors contributed to the study conception and design. Simulations and analysis were performed by ZW and YL. The first draft of the manuscript was written by ZW and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Yan Li.

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Wang, Z., Li, Y. Rigid spacecraft nonlinear robust \(H_\infty \) attitude controller design under actuator misalignments. Nonlinear Dyn 111, 15037–15054 (2023). https://doi.org/10.1007/s11071-023-08620-6

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