Constrained Station Relocation in Geostationary Equatorial Orbit Using a Legendre Pseudospectral Method

Kim, Seung Pil; Melton, Robert G.

doi:10.2514/1.g000114

Cited by 12 publications

(11 citation statements)

References 4 publications

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“…subject to the dynamic equations (38) and (15,16, and the boundary conditions (12) and (17,18, with the terminal time specified and the terminal states free. Then, the LPM method is used to convert the above optimal control problem into an approximate NLP problem.…”

Section: Lpm Methods and Nlp Problemmentioning

confidence: 99%

Multi-player nonzero-sum Nash differential game: variation and pseudo-spectral method

Zhou

Zhang

2016

Optim. Control Appl. Meth.

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Summary A novel method is presented to solve the nonzero‐sum multi‐player Nash differential game. It combines the use of the variation and Legendre pseudo‐spectral methods. By the variation method, the original game is converted into a regular optimal control problem, avoiding the need to solve the associated Hamilton–Jacobi equation. Then the latter problem is converted into a common nonlinear programming problem via the Legendre pseudo‐spectral method, by which the saddle‐point for the original game can be achieved accurately. As an illustration, the air combat between two pursuers and an evader is formulated as a nonzero‐sum differential game. The simulation results show that numerical solutions can converge to the saddle‐points from different initial conditions, which demonstrates the feasibility and validity of the proposed method. Because the solution process requires little computational time, this method will allow for the development of a real time air combat control strategy. In addition, the simulations show that if the initial states of the two pursuers are fixed, there is an optimal initial heading angle for the evader to delay the interception time most effectively. Copyright © 2016 John Wiley & Sons, Ltd.

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Section: Lpm Methods and Nlp Problemmentioning

confidence: 99%

Multi-player nonzero-sum Nash differential game: variation and pseudo-spectral method

Zhou

Zhang

2016

Optim. Control Appl. Meth.

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“…1 and 2, respectively, show the variation in semimajor axis and longitude induced by the J 22 perturbation as a function of transfer duration predicted by Eqs. (13) and (12). The longitude intervals in three cases are examined: 0-60°, 60-120°, and 120-180°.…”

Section: The Final Conditions As a Function Of Transfer Durationmentioning

confidence: 99%

“…(12) and (13) constitute an approximation, because λ¯0, λ¯f , andā are replaced by λ 0 , λ f , and a c , respectively, in deriving Eqs. (12) and (13).…”

Section: The Variation In Semimajor and Longitude Induced By Earth's mentioning

confidence: 99%

“…(12) and (13) constitute an approximation, because λ¯0, λ¯f , andā are replaced by λ 0 , λ f , and a c , respectively, in deriving Eqs. (12) and (13). This assumption is valid because the longitude change caused by the J 22 perturbation is still small relative to the total longitude change, and the semimajor axis change is also small compared to the synchronous semimajor axis of the GEO.…”

Section: The Variation In Semimajor and Longitude Induced By Earth's mentioning

confidence: 99%

“…However, there are few studies on minimum-fuel station change, especially taking into account the effects of perturbations, relative to the minimum-time problem [9,11,12], and perturbations are usually neglected in the previous analysis and design of low-thrust station change. Free and Babuska [13] made a general survey of practical station relocation in geostationary orbit, making use of then-available on-board electric propulsion.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Minimum-fuel station-change for geostationary satellites using low-thrust considering perturbations

Zhao

Zhang

2016

Acta Astronautica

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On-orbit servicing of geosynchronous satellites based on low-thrust transfers considering perturbations

2019

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Constrained Station Relocation in Geostationary Equatorial Orbit Using a Legendre Pseudospectral Method

Cited by 12 publications

References 4 publications

Multi-player nonzero-sum Nash differential game: variation and pseudo-spectral method

Multi-player nonzero-sum Nash differential game: variation and pseudo-spectral method

Minimum-fuel station-change for geostationary satellites using low-thrust considering perturbations

On-orbit servicing of geosynchronous satellites based on low-thrust transfers considering perturbations

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