Analytical fuel‐optimal impulsive reconfiguration of formation‐flying satellites: A revisit and new results

Li, Jing

doi:10.1002/oca.2408

Cited by 3 publications

(2 citation statements)

References 22 publications

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“…The point x = x is a free boundary. The conditions (34) and (35) imply that the optimal policy is of the following form, which is of course admissible, and is referred to as QVIcontrol [37,54]:…”

Section: Verificationmentioning

confidence: 99%

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Mathematical and numerical analyses of a stochastic impulse control model with imperfect interventions

Yoshioka

Yaegashi

2021

J.Math.Industry

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A stochastic impulse control problem with imperfect controllability of interventions is formulated with an emphasis on applications to ecological and environmental management problems. The imperfectness comes from uncertainties with respect to the magnitude of interventions. Our model is based on a dynamic programming formalism to impulsively control a 1-D diffusion process of a geometric Brownian type. The imperfectness leads to a non-local operator different from the many conventional ones, and evokes a slightly different optimal intervention policy. We give viscosity characterizations of the Hamilton–Jacobi–Bellman Quasi-Variational Inequality (HJBQVI) governing the value function focusing on its numerical computation. Uniqueness and verification results of the HJBQVI are presented and a candidate exact solution is constructed. The HJBQVI is solved with the two different numerical methods, an ordinary differential equation (ODE) based method and a finite difference scheme, demonstrating their consistency. Furthermore, the resulting controlled dynamics are extensively analyzed focusing on a bird population management case from a statistical standpoint.

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Section: Verificationmentioning

confidence: 99%

“…Deep mathematical analysis of the impulse control models of population dynamics and related models have been carried out [31,32]. Other important industrial problems, such as gene regulation [33] and satellite control [34,35], have been considered with the impulse control as well.…”

Section: Introductionmentioning

confidence: 99%

Mathematical and numerical analyses of a stochastic impulse control model with imperfect interventions

Yoshioka

Yaegashi

2021

J.Math.Industry

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Fully distributed finite-time adaptive robust time-varying formation-containment control for satellite formation

Jiang

Tian

et al. 2023

International Journal of Control

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Analytical Results to Fuel-optimal Spacecraft Formation Maneuver

Wang

Gong

et al. 2020

J. Phys.: Conf. Ser.

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In this study, analytical results are obtained for fuel-optimal spacecraft formation maneuver, including initialization and reconfiguration. The method consists of two stages. The first is parameterization of the problem and a new form of the problem is developed for simplicity. Second, the out-of-plane and in-plane maneuver are studied with the help of a useful inequality introduced and proved, the lower bound of the fuel consumption and the corresponding constraints of the control forces are derived and obtained. The result shows that the minimum total fuel consumption depends on the relative size parameters, and that the existence of optimal control algorithms depends upon the initial conditions. Numerical simulation of application proved the validity and efficiency of the proposed method, which can also be utilized in the maneuver of PCF.

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Analytical fuel‐optimal impulsive reconfiguration of formation‐flying satellites: A revisit and new results

Cited by 3 publications

References 22 publications

Mathematical and numerical analyses of a stochastic impulse control model with imperfect interventions

Mathematical and numerical analyses of a stochastic impulse control model with imperfect interventions

Fully distributed finite-time adaptive robust time-varying formation-containment control for satellite formation

Analytical Results to Fuel-optimal Spacecraft Formation Maneuver

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