Geodesic
Numerical method for solving a nonlinear time-optimal control problem with additive control
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 11, pp. 1843-1854 
G. V. Shevchenko. Numerical method for solving a nonlinear time-optimal control problem with additive control. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 11, pp. 1843-1854. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_11_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Nonlinear systems whose right-hand sides are divided by the state and control and are linear in control are considered. An iterative method is proposed for solving time-optimal control problems for such systems. The method is based on constructing finite sequences of adjacent simplexes with their vertices lying on the boundaries of reachability sets. For a controllable system, it is proved that the minimizing sequence converges to an $\varepsilon$-optimal solution in a finite number of iterations.

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