Abstract:
For linear systems with interval constraints, a method for computing a time-optimal control is proposed. The method is based on transforming a quasi-optimal control. The properties and features of the quasi-optimal control are examined. A technique is described for dividing the domain of initial conditions into reachable sets over different times and for approximating each set by a family of hyperplanes. An iterative method for computing an optimal control with interval constraints is developed. The convergence of the method is proved, and a sufficient condition for the convergence of the computational process is obtained. The radius of local quadratic convergence is found. Numerical results are presented.
Citation:
V. M. Aleksandrov, “Optimal control of linear systems with interval constraints”, Zh. Vychisl. Mat. Mat. Fiz., 55:5 (2015), 758–775; Comput. Math. Math. Phys., 55:5 (2015), 749–765
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\by V.~M.~Aleksandrov
\paper Optimal control of linear systems with interval constraints
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2015
\vol 55
\issue 5
\pages 758--775
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\transl
\jour Comput. Math. Math. Phys.
\yr 2015
\vol 55
\issue 5
\pages 749--765
\crossref{https://doi.org/10.1134/S0965542515050048}
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Linking options:
https://www.mathnet.ru/eng/zvmmf10200
https://www.mathnet.ru/eng/zvmmf/v55/i5/p758
This publication is cited in the following 5 articles:
S. Yu. Babich, N. N. Dikhtyaruk, “Load transfer from an infinite inhomogeneous stringer to a prestressed elastic strip clamped at one edge”, Int. Appl. Mech., 56:6 (2020), 708–716
N. N. Dikhtyaruk, O. V. Kurinenko, E. A. Poplavskaya, N. N. Samaruk, “Interaction between a finite stringer and two identical prestressed strips: contact problem”, Int. Appl. Mech., 55:1 (2019), 79–85
S. Yu. Babich, N. N. Dikhtyaruk, S. V. Degtyar, “Contact problem for two identical strips reinforced by periodically arranged fasteners with initial stresses”, Int. Appl. Mech., 55:6 (2019), 629–635
V. M. Aleksandrov, “Optimal resource consumption control with interval restrictions”, J. Appl. Industr. Math., 12:2 (2018), 201–212
V. B. Rudnitskii, N. N. Dikhtyaruk, “Interaction between an infinite stringer and two identical prestressed strips: contact problem”, Int. Appl. Mech., 53:2 (2017), 149–155
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