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Numerical method for solving a nonlinear time-optimal control problem with additive control

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Abstract

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 ɛ-optimal solution in a finite number of iterations.

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Authors and Affiliations

  1. Institute of Mathematics, Siberian Division, Russian Academy of Sciences, pr. Koptyuga 4, Novosibirsk, 630090, Russia

    G. V. Shevchenko

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  1. G. V. Shevchenko
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Correspondence to G. V. Shevchenko.

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Original Russian Text © G.V. Shevchenko, 2007, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2007, Vol. 47, No. 11, pp. 1843–1854.

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Shevchenko, G.V. Numerical method for solving a nonlinear time-optimal control problem with additive control. Comput. Math. and Math. Phys. 47, 1768–1778 (2007). https://doi.org/10.1134/S0965542507110048

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