Abstract:
We study extremum norm problems for the terminal state of a linear dynamical system using methods of parameterization of admissible controls.
Piecewise continuous controls are approximated in the class of piecewise linear functions on a uniform grid of nodes of the time interval by linear combinations of special support functions. In this case, the restriction of a control of the original problem to the interval induces the same restrictions for the variables of the finite-dimensional problems.
The finite-dimensional version of a minimum norm problem can effectively be resolved with the help of modern convex optimization programs. In the case of two variables, we propose an analytical method of resolution that uses a one-dimensional minimization problem for a parabola over a segment.
For a non-convex norm maximization problem, the finite-dimensional version is resolved globally by exhaustive search over the vertices of a hypercube. The proposed approach provides further insights into global resolution of non-convex optimal control problems and is exemplified by some illustrative problems.
Keywords:
linear control system, extremum norm problems for the terminal state, piecewise linear approximation, finite-dimensional problems.
Citation:
V. A. Srochko, E. V. Aksenyushkina, “On resolution of an extremum norm problem for the terminal state of a linear system”, Bulletin of Irkutsk State University. Series Mathematics, 34 (2020), 3–17
\Bibitem{SroAks20}
\by V.~A.~Srochko, E.~V.~Aksenyushkina
\paper On resolution of an extremum norm problem for the terminal state of a linear system
\jour Bulletin of Irkutsk State University. Series Mathematics
\yr 2020
\vol 34
\pages 3--17
\mathnet{http://mi.mathnet.ru/iigum431}
\crossref{https://doi.org/10.26516/1997-7670.2020.34.3}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000599772800001}
Linking options:
https://www.mathnet.ru/eng/iigum431
https://www.mathnet.ru/eng/iigum/v34/p3
This publication is cited in the following 4 articles:
V. A. Srochko, E. V. Aksenyushkina, “Parametricheskaya transformatsiya kvadratichnogo funktsionala v lineinoi sisteme upravleniya”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 48 (2024), 21–33
B. I. Ananyev, P. A. Yurovskikh, “About an estimation problem of a linear system with delay of information”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 42 (2022), 3–16
V. A. Srochko, E. V. Aksenyushkina, V. G. Antonik, “Reshenie lineino-kvadratichnoi zadachi optimalnogo upravleniya na osnove konechnomernykh modelei”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 37 (2021), 3–16
A V Arguchintsev, M S Kedrina, “Determination of functional parameters in boundary conditions of linear hyperbolic systems by optimal control methods”, J. Phys.: Conf. Ser., 1847:1 (2021), 012014
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