Method for solving an optimal control problem in the Mayer form with a quasidifferentiable functional in the presence of phase constraints
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 19 (2023) no. 1, pp. 120-134
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The article considers the problem of optimal control of an object described by a system of ordinary differential equations with a continuously differentiable right-hand side and with a nonsmooth (but only a quasidifferentiable) quality functional. The problem is in the Mayer form with either free or partially fixed right end. Piecewise-continuous and bounded controls are supposed to be admissible if they lie in some parallelepiped at any moment of time. The phase coordinates and controls are also subject to mixed pointwise constraints. Phase constraints are taken into account by introducing new variables with known boundary conditions into the system. The standard discretization of the original system and the parametrization of the control are carried out, theorems are given on the convergence of the solution of the discrete system obtained to the desired solution of the continuous problem. Further, in order to study the resulting discrete system, the apparatus of quasidifferential calculus is used and the method of the quasidifferential descent is applied. Examples illustrating the operation of the algorithm are given.
Keywords:
optimal control, Mayer problem, nonsmooth optimization, quasidifferential, phase constraints.
@article{VSPUI_2023_19_1_a9,
author = {A. V. Fominykh and V. V. Karelin and L. N. Polyakova},
title = {Method for solving an optimal control problem in the {Mayer} form with a quasidifferentiable functional in the presence of phase constraints},
journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
pages = {120--134},
publisher = {mathdoc},
volume = {19},
number = {1},
year = {2023},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VSPUI_2023_19_1_a9/}
}
TY - JOUR AU - A. V. Fominykh AU - V. V. Karelin AU - L. N. Polyakova TI - Method for solving an optimal control problem in the Mayer form with a quasidifferentiable functional in the presence of phase constraints JO - Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ PY - 2023 SP - 120 EP - 134 VL - 19 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/VSPUI_2023_19_1_a9/ LA - ru ID - VSPUI_2023_19_1_a9 ER -
%0 Journal Article %A A. V. Fominykh %A V. V. Karelin %A L. N. Polyakova %T Method for solving an optimal control problem in the Mayer form with a quasidifferentiable functional in the presence of phase constraints %J Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ %D 2023 %P 120-134 %V 19 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/VSPUI_2023_19_1_a9/ %G ru %F VSPUI_2023_19_1_a9
A. V. Fominykh; V. V. Karelin; L. N. Polyakova. Method for solving an optimal control problem in the Mayer form with a quasidifferentiable functional in the presence of phase constraints. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 19 (2023) no. 1, pp. 120-134. http://geodesic.mathdoc.fr/item/VSPUI_2023_19_1_a9/