Asymptotics of a Solution to an Optimal Control Problem with a Terminal Convex Performance Index and a Perturbation of the Initial Data

In this paper, we investigate a problem of optimal control over a finite time interval for a linear system with constant coefficients and a small parameter in the initial data in the class of piecewise continuous controls with smooth geometric constraints. We consider a terminal convex performance i...

Full description

Saved in:
Bibliographic Details
Published inProceedings of the Steklov Institute of Mathematics Vol. 323; no. Suppl 1; pp. S85 - S97
Main Authors Danilin, A. R., Kovrizhnykh, O. O.
Format Journal Article Conference Proceeding
LanguageEnglish
Published Moscow Pleiades Publishing 01.12.2023
Springer Nature B.V
Subjects
Asymptotic properties
Geometric constraints
Mathematics
Mathematics and Statistics
Optimal control
Parameters
Performance indices
Rational functions
terminal convex performance index
optimal control
asymptotic expansion
small parameter
Online AccessGet full text
ISSN0081-5438
1531-8605
DOI10.1134/S008154382306007X

Cover

More Information
Summary:In this paper, we investigate a problem of optimal control over a finite time interval for a linear system with constant coefficients and a small parameter in the initial data in the class of piecewise continuous controls with smooth geometric constraints. We consider a terminal convex performance index. We substantiate the limit relations as the small parameter tends to zero for the optimal value of the performance index and for the vector generating the optimal control in the problem. We show that the asymptotics of the solution can be of complicated nature. In particular, it may have no expansion in the Poincaré sense in any asymptotic sequence of rational functions of the small parameter or its logarithms.
Bibliography:ObjectType-Article-1
ObjectType-Feature-2
SourceType-Conference Papers & Proceedings-1
content type line 22
ISSN:0081-5438
1531-8605
DOI:10.1134/S008154382306007X