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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2026. Vol 56

A Technique of Nonlocal Search in Optimal Control Problems Based on the Hidden Convexity Property

Author(s)

Tatiana S. Zarodnyuk

Matrosov Institute for System Dynamics and Control Theory SB RAS, Irkutsk, Russian Federation

Abstract
A non-local search method for extremum in nonlinear optimal control problems is developed, based on the use of the property of hidden convexity of the set of admissible velocities of controlled dynamic systems. Extended optimal control problems are formed, which in some cases can be characterized by convex reachable sets. Five variants of the convexification method of the initial optimal control problem are proposed, depending on the way of accounting for the constraints on auxiliary controls. The results of computational experiments on a test collection of nonlinear optimal control problems with geometric constraints are presented. Conclusions are formulated based on the obtained experimental experience and the use of the expansion correctness criterion. The proposed approach allows for the convexification of the velocity set and expands the applicability of numerical optimization methods in the study of non-convex optimal control problems.
About the Authors
Tatiana S. Zarodnyuk, Cand. Sci. (Tech.), Senior Research Scientist, Matrosov Institute for System Dynamics and Control Theory SB RAS, Irkutsk, 664033, Russian Federation, tz@icc.ru
For citation
Zarodnyuk T. S. A Technology of Nonlocal Search in Optimal Control Problems Based on the Hidden Convexity Property. The Bulletin of Irkutsk State University. Series Mathematics, 2026, vol. 56, pp. 19–32. (in Russian) https://doi.org/10.26516/1997-7670.2026.56.19
Keywords
nonlinear optimal control problem, hidden convexity property, Gamkrelidze extension, admissible velocities set
UDC
517.977
MSC
49J15, 49M37, 90C26
DOI
https://doi.org/10.26516/1997-7670.2026.56.19
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