naa a22 4500 510774164 CHVBK 20180411083224.0 cr unu---uuuuu 180411e20131201xx s 000 0 eng 10.1007/s40295-015-0050-4 doi (NATIONALLICENCE)springer-10.1007/s40295-015-0050-4 A Magnus Series-Based Modified Sweep Method for Optimal Control [Elektronische Daten] [D. Cho, Srinivas Vadali] 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. American Astronautical Society, 2015 Optimal control nationallicence Discretization nationallicence Magnus integrator nationallicence Cho D. Department of Aerospace Engineering, Texas A&M University, 77843-3141, College Station, TX, USA aut Vadali Srinivas Department of Aerospace Engineering, Texas A&M University, 77843-3141, College Station, TX, USA aut The Journal of the Astronautical Sciences Springer US; http://www.springer-ny.com 60/3-4(2013-12-01), 313-336 0021-9142 60:3-4<313 2013 60 40295 https://doi.org/10.1007/s40295-015-0050-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s40295-015-0050-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Cho D. Department of Aerospace Engineering, Texas A&M University, 77843-3141, College Station, TX, USA aut NATIONALLICENCE 700 1- Vadali Srinivas Department of Aerospace Engineering, Texas A&M University, 77843-3141, College Station, TX, USA aut NATIONALLICENCE 773 0- The Journal of the Astronautical Sciences Springer US; http://www.springer-ny.com 60/3-4(2013-12-01), 313-336 0021-9142 60:3-4<313 2013 60 40295 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer