Abstract:
A numerical approach is applied to the maximization of a positive definite quadratic form on the set of terminal states of a linear system with interval constraints on the control. An optimality criterion is used to develop a method for nonlocal improvement of controls satisfying the maximum principle (extreme points of the reachable set). The iterative procedure of the method is proved to converge. Numerical results are presented.
Citation:
V. G. Antonik, V. A. Srochko, “Method for nonlocal improvement of extreme controls in the maximization of the terminal state norm”, Zh. Vychisl. Mat. Mat. Fiz., 49:5 (2009), 791–804; Comput. Math. Math. Phys., 49:5 (2009), 762–775
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\by V.~G.~Antonik, V.~A.~Srochko
\paper Method for nonlocal improvement of extreme controls in the maximization of the terminal state norm
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2009
\vol 49
\issue 5
\pages 791--804
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\transl
\jour Comput. Math. Math. Phys.
\yr 2009
\vol 49
\issue 5
\pages 762--775
\crossref{https://doi.org/10.1134/S0965542509050030}
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Linking options:
https://www.mathnet.ru/eng/zvmmf4685
https://www.mathnet.ru/eng/zvmmf/v49/i5/p791
This publication is cited in the following 9 articles:
V. A. Srochko, E. V. Aksenyushkina, “On resolution of an extremum norm problem for the terminal state of a linear system”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 34 (2020), 3–17
Antonik V.G. Arguchintsev A.V., “To the 75Th Anniversary of the Birth of Professor V. a. Srochko”, Bull. Irkutsk State Univ.-Ser. Math., 34 (2020), 126–134
E. V. Aksenyushkina, V. A. Srochko, “Sufficient optimality conditions for a class of nonconvex control problems”, Comput. Math. Math. Phys., 55:10 (2015), 1642–1652
V. N. Zhermolenko, “On maximal deviation of linear system”, Autom. Remote Control, 73:7 (2012), 1117–1125
O. V. Morzhin, “Metody nelokalnogo uluchsheniya v zadachakh optimalnogo upravleniya na osnove tochnykh formul prirascheniya”, Programmnye sistemy: teoriya i prilozheniya, 1:4 (2010), 67–83
V. A. Srochko, S. N. Ushakova, “Improvement of extreme controls and the steepest ascent method in the norm maximization problem on the reachable set”, Comput. Math. Math. Phys., 50:5 (2010), 805–815
Srochko V.A., Rozinova N.S., “Uslovie optimalnosti i metod poiska ekstremalnykh tochek v zadache na maksimum ellipsoidalnoi normy”, Izv. Irkutskogo gos. un-ta. Ser.: Matem., 2010, no. 3, 93–104
V. A. Srochko, N. S. Rozinova, “Uslovie optimalnosti i metod poiska ekstremalnykh tochek v zadache na maksimum ellipsoidalnoi normy”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 3:3 (2010), 93–104
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