title: On numerical solution of the optimal control problem based on a method using the second variation of a trajectory
metadata.name: dc.contributor.author
metadata.value: Drivotin, Oleg I.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2019-07-17T12:37:06Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2019-07-17T12:37:06Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2019-06
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Drivotin O. I. On numerical solution of the optimal control problem based on a method using the second variation of a trajectory. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2019, vol. 15, iss. 2, pp. 283–295.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu10.2019.211
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/15961
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: A new approach for the numerical solution of the optimal control problem is presented. This approach is based on the parametrization of the control function and computation of the first and the second derivatives of the cost functional over parameters. Computation of the second derivatives is carried out using an integral representation for the second variation of the trajectory of a controlled dynamical system,which is obtained in this work and includes a tensor of the third rank. The proposed approach differs from the approach being used previously, in which the second derivatives of the cost functional are expressed through the matrix momenta. A numerical method based on the second variation of the trajectory can be effective in problems with a great number of parameters. Using the matrix  momenta, one should integrate a system of differential equations, the number of which is quadratic in the number of parameters. In the present approach, the number of the equation to be integrated is determined only by the dimension of the phase space and can be sufficiently smaller.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Applied Mathematics. Computer Science. Control Processes;Volume 15; Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: optimal control
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: controlled dynamical system
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: second variation
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: numerical methods of the second order
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On numerical solution of the optimal control problem based on a method using the second variation of a trajectory
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 283-295.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/15961/1/283-295.pdf
resources.format: Adobe PDF
resources.size: 295,5 kB