Method of continuation for optimization of interplanetary low-thrust trajectories

Petukhov, V. G.

doi:10.1134/s0010952512030069

Cited by 49 publications

(10 citation statements)

References 4 publications

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“…The essence of the parameter continuation method lies at the formal reduction of the considered boundary value problem to the Cauchy problem [4][5][6][7]. The boundary problem for a dynamic system with boundary conditions can be represented as an equation for the residuals at the right end of the trajectory:…”

Section: Parameter Continuation Methodsmentioning

confidence: 99%

“…This method burgeons results in a quick manner in case of restricted control and variable boundaries. For better application of the numerical method, the authors convert the optimal control problem to the boundary problem, the parameter continuation method [3][4][5][6][7] is used to successfully handle the boundary problem. The simulation results show that the UAV lands with different speed values and the control is within the allowable range.…”

Section: Introductionmentioning

confidence: 99%

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Auto-Transformations of the Probability Density Functions

Harin¹

2021

AJAMS

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The two goals of the present article are: 1) To define transformations (named here as auto-transformations) of the probability density functions (PDFs) of random variables into some similar functions having smaller sizes of their domains. 2) To research and outline basic features of these auto-transformations of PDFs. Particularly, auto-transformations from infinite to finite domains are analyzed. The goals are caused by the well-known problems of behavioral sciences.

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Section: Parameter Continuation Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Auto-Transformations of the Probability Density Functions

Harin¹

2021

AJAMS

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“…A great deal of research has been done previously on the design of low-thrust orbital transfers [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]. Refs.…”

Section: Introductionmentioning

confidence: 99%

“…Refs. [3,4,5,6] solved minimum-fuel optimal control problems by solving the Hamiltonian boundary-value problem (HBVP) arising from the calculus of variations. In particular, Ref.…”

Section: Introductionmentioning

confidence: 99%

Minimum-Time Earth-to-Mars Interplanetary Orbit Transfer Using Adaptive Gaussian Quadrature Collocation

Holden¹,

He²,

Rao³

2020

Preprint

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“…A single engine is assumed to operate at effective constant specific impulse and efficiency values [26,27,28,29,30]. However, the actual performance of SEP systems depends on the input power, which has to be taken into consideration for obtaining more realistic trajectories [31,32,33,34,35,36,37,38,39,40]. More accurate knowledge of the capability of a spacecraft to change its trajectory is obtained when more realistic models of the SEP system and dynamics are used [41,42,43].…”

mentioning

confidence: 99%

A novel approach for optimal trajectory design with multiple operation modes of propulsion system, part 2

et al. 2020

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Equipping a spacecraft with multiple solar-powered electric engines (of the same or different types) compounds the task of optimal trajectory design due to presence of both real-valued inputs (power input to each engine in addition to the direction of thrust vector) and discrete variables (number of active engines).Each engine can be switched on/off independently and "optimal" operating power of each engine depends on the available solar power, which depends on the distance from the Sun. Application of the Composite Smooth Control (CSC) framework to a heliocentric fuel-optimal trajectory optimization from the Earth to the comet 67P/Churyumov-Gerasimenko is demonstrated, which presents a new approach to deal with multiple-engine problems. Operation of engine clusters with 4, 6, 10 and even 20 engines of the same type can be optimized.Moreover, engine clusters with different/mixed electric engines are considered with either 2, 3 or 4 different types of engines. Remarkably, the CSC framework allows us 1) to reduce the original multi-point boundary-value problem to a two-point boundary-value problem (TPBVP), and 2) to solve the resulting TP-BVPs using a single-shooting solution scheme and with a random initialization of the missing costates. While the approach we present is a continuous neighbor of the discontinuous extremals, we show that the discontinuous necessary conditions are satisfied in the asymptotic limit. We believe this is the first indirect method to accommodate a multi-mode control of this level of complexity with realistic engine performance curves. The results are interesting and promising for dealing with a large family of such challenging multi-mode optimal control problems.

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Method of continuation for optimization of interplanetary low-thrust trajectories

Cited by 49 publications

References 4 publications

Auto-Transformations of the Probability Density Functions

Auto-Transformations of the Probability Density Functions

Minimum-Time Earth-to-Mars Interplanetary Orbit Transfer Using Adaptive Gaussian Quadrature Collocation

A novel approach for optimal trajectory design with multiple operation modes of propulsion system, part 2

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