Метод решения задачи оптимального управления в форме Майера с квазидифференцируемым функционалом при наличии фазовых ограничений

Alexander V. Fominyh; Vladimir V. Karelin; Lyudmila N. Polyakova

doi:10.21638/11701/spbu10.2023.110

Authors

Alexander V. Fominyh St Petersburg State University, 7-9, Universitetskaya nab., St Petersburg, 199034, Russian Federation https://orcid.org/0000-0002-0178-8384
Vladimir V. Karelin St Petersburg State University, 7-9, Universitetskaya nab., St Petersburg, 199034, Russian Federation
Lyudmila N. Polyakova St Petersburg State University, 7-9, Universitetskaya nab., St Petersburg, 199034, Russian Federation

DOI:

https://doi.org/10.21638/11701/spbu10.2023.110

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

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References

Литература

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