Geodesic
Approximation of attainability sets and calculation of time-optimal control in real time
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 8 (2011), pp. 72-104

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A new approach to realization of time-optimal control in real time for linear systems under control with constraint is proposed. It is based on subdividing the computational costs on those made in advance of the control process and those carried as it proceeds. The preliminary computations do nit depend on actual initial condition and rely on approximation of attainability sets in different periods of time by complex of hyperplane. Methods of constructing them are given with a way to single out the support hyperplane. Methods of approximate finding and following correction for normalized vector of adjoint system initial conditions, switching times of time-optimal control, and the control completion time are suggested. Estimation of computational working time is given. Reduction of unspecified form systems to their canonical form is considered. Quantitative measure of total controllability is deter-mined. Results of modeling and numerical calculations are presented.
Keywords: optimal control, speed, attainability sets, hyperplane, real time, adjoint system, initial condition, edge point, first approximation, approximating construction, computational costs. 
@article{SEMR_2011_8_a7,
     author = {V. M. Aleksandrov},
     title = {Approximation of attainability sets and calculation of time-optimal control in real time},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {72--104},
     publisher = {mathdoc},
     volume = {8},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2011_8_a7/}
}
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V. M. Aleksandrov. Approximation of attainability sets and calculation of time-optimal control in real time. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 8 (2011), pp. 72-104. http://geodesic.mathdoc.fr/item/SEMR_2011_8_a7/