Dynamics Near the Three-Body Libration Points via Koopman Operator Theory

Servadio, Simone; Arnas, David; Linares, Richard

doi:10.2514/1.g006519

Cited by 10 publications

(3 citation statements)

References 29 publications

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“…A related problem is lunar stationkeeping, namely for Lyapunov and Halo orbits in the circularrestricted three-body problem (CR3BP). One study creatively obtained the Koopman operator approximation of the system matrix through direct computation using Legendre polynomials, which are already by their nature a complete and finite set of orthonormal basis in Hilbert space [15]. See [102] for more information on the CR3BP.…”

Section: Space Systemsmentioning

confidence: 99%

Vehicular Applications of Koopman Operator Theory—A Survey

2023

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Koopman operator theory has proven to be a promising approach to nonlinear system identification and global linearization. For nearly a century, there had been no efficient means of calculating the Koopman operator for applied engineering purposes. The introduction of a recent computationally efficient method in the context of fluid dynamics, which is based on the system dynamics decomposition to a set of normal modes in descending order, has overcome this long-lasting computational obstacle. The purely data-driven nature of Koopman operators holds the promise of capturing unknown and complex dynamics for reduced-order model generation and system identification, through which the rich machinery of linear control techniques can be utilized. Given the ongoing development of this research area and the many existing open problems in the fields of smart mobility and vehicle engineering, a survey of techniques and open challenges of applying Koopman operator theory to this vibrant area is warranted. This review focuses on the various solutions of the Koopman operator which have emerged in recent years, particularly those focusing on mobility applications, ranging from characterization and component-level control operations to vehicle performance and fleet management. Moreover, this comprehensive review of over 100 research papers highlights the breadth of ways Koopman operator theory has been applied to various vehicular applications with a detailed categorization of the applied Koopman operator-based algorithm type. Furthermore, this review paper discusses theoretical aspects of Koopman operator theory that have been largely neglected by the smart mobility and vehicle engineering community and yet have large potential for contributing to solving open problems in these areas.

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Section: Space Systemsmentioning

confidence: 99%

Vehicular Applications of Koopman Operator Theory—A Survey

2023

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“…84 While the Koopman operator continues to gain popularity, attaining high accuracy frequently involves accounting for the substantial dimensionality of the observables, which, unfortunately, leads to higher computational costs. 82 The development of DAC aims to bridge the gap in utilizing data for practical aerial applications in control systems, ensuring safety and logical operation. It ensures safety by activating only when the primary controller encounters deteriorating conditions, allowing the pilot to decide whether to activate it or not.…”

Section: Introductionmentioning

confidence: 99%

“…In DAC, the Koopman estimator plays a pivotal role in data‐based linearization within the observable space, 79 while the nonlinear control leverages the structural properties of the nonlinear model to enable stability, observability, and performance analysis rigorously. In recent years, the Koopman operator and Koopman linearization successfully have been applied in many aerial and space applications such as low‐thrust trajectory optimization, 80 attitude control of spacecraft, 81 studying the motion of a satellite close to a libration point, 82 approximating analytical solution for Zonal Harmonics problem, 83 and decision making 84 . While the Koopman operator continues to gain popularity, attaining high accuracy frequently involves accounting for the substantial dimensionality of the observables, which, unfortunately, leads to higher computational costs 82 …”

Section: Introductionmentioning

confidence: 99%

Data‐assisted control: A framework development by exploiting NASA Generic Transport platform

Eslami,

Banazadeh

2023

Intl J Robust & Nonlinear

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The increasing capabilities of control systems, driven by abundant data and computational resources, necessitate the incorporation of data‐based techniques with model‐based approaches. While mathematical models exist for air and space vehicles, they may not fully meet the requirements for expanding control system capabilities. Consequently, the development of data‐based extensions in collaboration with these models becomes crucial to provide specific analysis and synthesis tools in the hybrid realm for practical cases. This article introduces the data‐assisted control (DAC) framework for aerospace vehicles, with the NASA generic transport model serving as the platform for study. By leveraging data, the model‐based controller enhances performance during a damage event. Real‐time decisions are made to update the control law based on information obtained from the data, while the model‐based controller may not exhibit consistent performance. The closed‐loop system is shown to be stable in the transition phase between the data and the model, and robust against uncertainties. The dual unscented Kalman filter is employed to estimate fixed dynamic parameters and generalized force‐moment, and the Koopman estimator is used to estimate the evolution equation of the estimated forces and moments. The dual estimation model ensures observability by considering the persistency of excitation. Simulations have shown that the purely model‐based robust control leads to degradation of the closed‐loop performance in case of damage, suggesting the need for data assistance. The DAC framework offers a robust approach to integrate data and models, significantly enhancing control performance in practical aerospace applications.

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