Geodesic
Numerical methods for solving terminal optimal control problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 2, pp. 224-237

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Numerical methods for solving optimal control problems with equality constraints at the right end of the trajectory are discussed. Algorithms for optimal control search are proposed that are based on the multimethod technique for finding an approximate solution of prescribed accuracy that satisfies terminal conditions. High accuracy is achieved by applying a second-order method analogous to Newton's method or Bellman's quasilinearization method. In the solution of problems with direct control constraints, the variation of the control is computed using a finite-dimensional approximation of an auxiliary problem, which is solved by applying linear programming methods. 
@article{ZVMMF_2016_56_2_a4,
     author = {A. Yu. Gornov and A. I. Tyatyushkin and E. A. Finkelshtein},
     title = {Numerical methods for solving terminal optimal control problems},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {224--237},
     publisher = {mathdoc},
     volume = {56},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_2_a4/}
}
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A. Yu. Gornov; A. I. Tyatyushkin; E. A. Finkelshtein. Numerical methods for solving terminal optimal control problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 2, pp. 224-237. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_2_a4/