Vestnik Sankt-Peterburgskogo Universiteta. Seriya 10. Prikladnaya Matematika. Informatika. Protsessy Upravleniya
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Vestnik Sankt-Peterburgskogo Universiteta. Seriya 10. Prikladnaya Matematika. Informatika. Protsessy Upravleniya, 2023, Volume 19, Issue 1, Pages 120–134
DOI: https://doi.org/10.21638/11701/spbu10.2023.110
(Mi vspui571)
 

Control processes

Method for solving an optimal control problem in the Mayer form with a quasidifferentiable functional in the presence of phase constraints

A. V. Fominykh, V. V. Karelin, L. N. Polyakova

St. Petersburg State University, 7–9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation
References:
Abstract: 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.
Funding agency Grant number
Russian Science Foundation 21-71-00021
\indent $^{*}$ The main results of the paper (items 3–6) are obtained by Alexander V. Fominyh, the work is supported by the Russian Science Foundation (grant N 21-71-00021).
Received: November 1, 2022
Accepted: January 19, 2023
Document Type: Article
UDC: 517.977.1
MSC: 49M
Language: Russian
Citation: 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 S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 19:1 (2023), 120–134
Citation in format AMSBIB
\Bibitem{FomKarPol23}
\by A.~V.~Fominykh, V.~V.~Karelin, L.~N.~Polyakova
\paper Method for solving an optimal control problem in the Mayer form with a quasidifferentiable functional in the presence of phase constraints
\jour Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr.
\yr 2023
\vol 19
\issue 1
\pages 120--134
\mathnet{http://mi.mathnet.ru/vspui571}
\crossref{https://doi.org/10.21638/11701/spbu10.2023.110}
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