Geodesic
Improvement of extreme controls and the steepest ascent method in the norm maximization problem on the reachable set
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 5, pp. 848-859

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The maximization of the terminal state norm of a linear system is considered in the sense of searching for and improving extreme points of the reachable set. A sufficient optimality condition is formulated in terms of a special maximum function. A steepest ascent method for level surfaces of the objective function is constructed, and related procedures for improving extreme controls are described. 
@article{ZVMMF_2010_50_5_a5,
     author = {V. A. Srochko and S. N. Ushakova},
     title = {Improvement of extreme controls and the steepest ascent method in the norm maximization problem on the reachable set},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {848--859},
     publisher = {mathdoc},
     volume = {50},
     number = {5},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_5_a5/}
}
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V. A. Srochko; S. N. Ushakova. Improvement of extreme controls and the steepest ascent method in the norm maximization problem on the reachable set. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 5, pp. 848-859. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_5_a5/