A Magnus Series-Based Modified Sweep Method for Optimal Control

Autor:	Srinivas R. Vadali, D. H. Cho
Rok vydání:	2013
Předmět:	Hessian matrix Discretization Differential equation Mathematical analysis MathematicsofComputing_NUMERICALANALYSIS Aerospace Engineering Optimal control Convexity symbols.namesake Nonlinear system Space and Planetary Science Magnus expansion Convergence (routing) symbols Mathematics
Zdroj:	The Journal of the Astronautical Sciences. 60:313-336
ISSN:	2195-0571 0021-9142
DOI:	10.1007/s40295-015-0050-4
Popis:	This paper presents variations of the Successive Backward Sweep (SBS) method for solving nonlinear optimal control problems with terminal constraints. The state-costate differential equations are linearized and discretized explicitly in time by a truncated Magnus series representation of the state transition. These discrete exponential maps are propagated, backwards in time, by the sweep method. Two variants of the method are implemented to test for the Jacobi sufficient condition and achieve convergence to local optimal solutions. Where required, the problems are regularized to ensure satisfaction of the convexity conditions by modifying the associated Hessian. The performance of the Magnus series-based SBS method is compared with that of a non-symplectic 5 th order Runge-Kutta method on three examples: a highly nonlinear, two-dimensional problem, a hypersensitive problem, and an atmospheric reentry guidance problem.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::7f12556b5fedd3d3f90592b2b8d2c279 https://doi.org/10.1007/s40295-015-0050-4 Zobrazit plný text záznamu Full text from SpringerLink