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Bibliographic description:
Srochko V. A.
,
Aksenyushkina E. V.
,
Antonik V. G.
FINITE-DIMENSIONAL APPROXIMATION OF CONTROLS IN OPTIMIZATION PROBLEMS FOR LINEAR SYSTEMS // BSU bulletin. Mathematics, Informatics. - 2020. №3. . - С. 19-31.
Title:
FINITE-DIMENSIONAL APPROXIMATION OF CONTROLS IN OPTIMIZATION PROBLEMS FOR LINEAR SYSTEMS
Financing:
Codes:
DOI: 10.18101/2304-5728-2020-3-19-31UDK: 517.977
Annotation:
The article studies extremum problems of the final state norm of a linear
dynamical system using methods of parameterization of admissible controls. Piecewise
continuous controls are approximated in the class of piecewise constant 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 problems of the final state norm; piecewise constant approximation; finite-dimensional problems.
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