Abstract:
Two control problems for a state-linear control system are considered: the minimization of a terminal functional representable as the difference of two convex functions (d.c. functions) and the minimization of a convex terminal functional with a d.c. terminal inequality contraint. Necessary and sufficient global optimality conditions are proved for problems in which the Pontryagin and Bellman maximum principles do not distinguish between locally and globally optimal processes. The efficiency of the approach is illustrated by examples.
Key words:
optimal control, locally and globally optimal processes, optimality principles and conditions.
Citation:
A. S. Strekalovskii, “Optimal control problems with terminal functionals represented as the difference of two convex functions”, Zh. Vychisl. Mat. Mat. Fiz., 47:11 (2007), 1865–1879; Comput. Math. Math. Phys., 47:11 (2007), 1788–1801
\Bibitem{Str07}
\by A.~S.~Strekalovskii
\paper Optimal control problems with terminal functionals represented as the difference of two convex functions
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2007
\vol 47
\issue 11
\pages 1865--1879
\mathnet{http://mi.mathnet.ru/zvmmf221}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2405031}
\transl
\jour Comput. Math. Math. Phys.
\yr 2007
\vol 47
\issue 11
\pages 1788--1801
\crossref{https://doi.org/10.1134/S0965542507110061}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-36448981437}
Linking options:
https://www.mathnet.ru/eng/zvmmf221
https://www.mathnet.ru/eng/zvmmf/v47/i11/p1865
This publication is cited in the following 10 articles:
Tatiana V. Gruzdeva, Alexander S. Strekalovsky, Lecture Notes in Computer Science, 12095, Mathematical Optimization Theory and Operations Research, 2020, 115
Gornov A.Yu., Zarodnyuk T.S., “Computational Technology For Solving Nonconvex Optimal Control Problems For Power Systems”, Proceedings of the Vth International Workshop Critical Infrastructures: Contingency Management, Intelligent, Agent-Based, Cloud Computing and Cyber Security (Iwci 2018), Advances in Intelligent Systems Research, 158, eds. Massel L., Makagonova N., Kopaygorodsky A., Massel A., Atlantis Press, 2018, 68–72
Strekalovsky A.S. Yanulevich M.V., “on Global Search in Nonconvex Optimal Control Problems”, J. Glob. Optim., 65:1, SI (2016), 119–135
A. S. Strekalovskii, “Sovremennye metody resheniya nevypuklykh zadach optimalnogo upravleniya”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 8 (2014), 141–163
Strekalovsky A.S., “Global Optimality Conditions for Optimal Control Problems with Functions of Ad Alexandrov”, J. Optim. Theory Appl., 159:2 (2013), 297–321
Strekalovsky A.S. Yanulevich M.V., “Global Search in a Noncovex Optimal Control Problem”, J. Comput. Syst. Sci. Int., 52:6 (2013), 893–908
A. S. Strekalovsky, “Maximizing a state convex Lagrange functional in optimal control”, Autom. Remote Control, 73:6 (2012), 949–961
V. G. Antonik, V. A. Srochko, “Method for nonlocal improvement of extreme controls in the maximization of the terminal state norm”, Comput. Math. Math. Phys., 49:5 (2009), 762–775
A. S. Strekalovskii, M. V. Yanulevich, “Global search in the optimal control problem with a terminal objective functional represented as the difference of two convex functions”, Comput. Math. Math. Phys., 48:7 (2008), 1119–1132
Citation in format AMSBIB
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