A multiple-shooting differential dynamic programming algorithm. Part 1: Theory

Multiple-shooting benefits a wide variety of optimal control algorithms by alleviating large sensitivities present in highly nonlinear problems, improving robustness to initial guesses, and increasing the potential for parallel implementation. In this paper series, motivated by the challenges of opt...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:Acta astronautica Ročník 170; s. 686 - 700
Hlavní autoři: Pellegrini, Etienne, Russell, Ryan P.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elmsford Elsevier Ltd 01.05.2020
Elsevier BV
Témata:
Algorithms
Augmented Lagrangian
Control algorithms
Differential dynamic programming
Dynamic programming
Initial conditions
Multiple-shooting
Nonlinear programming
Optimal control
Spacecraft
Spacecraft trajectories
Terminal constraints
Trajectory optimization
Multiple-shooting
Differential dynamic programming
Optimal control
Trajectory optimization
Augmented Lagrangian
ISSN:0094-5765, 1879-2030
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Popis
Shrnutí:Multiple-shooting benefits a wide variety of optimal control algorithms by alleviating large sensitivities present in highly nonlinear problems, improving robustness to initial guesses, and increasing the potential for parallel implementation. In this paper series, motivated by the challenges of optimizing highly sensitive spacecraft trajectories, the multiple-shooting approach is embedded for the first time in the formulation of a Differential Dynamic Programming algorithm. Contrary to traditional nonlinear programming methods which necessitate minimal modification of the formulation in order to incorporate multiple-shooting principles, DDP requires novel non-trivial derivations, in order to include the initial conditions of the multiple-shooting subintervals and track their sensitivities. The initial conditions are updated in a necessary additional algorithmic step. A null-space trust-region method is used for the solution of the quadratic subproblems, and equality and inequality path and terminal constraints are handled through a general augmented Lagrangian approach. The propagation of the trajectory and the optimization of its controls are decoupled through the use of State-Transition Matrices. Part 1 of the paper series provides the necessary theoretical developments and implementation details for the algorithm. Part 2 contains validation and application cases. •The multiple-shooting framework is applied to Differential Dynamic Programming.•The necessary quadratic expansions feedback control laws are developed.•An Augmented Lagrangian approach is applied for equality and inequality constraints.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0094-5765
1879-2030
DOI:10.1016/j.actaastro.2019.12.037