This article is cited in 4 papers

Dynamic systems and optimal control

On resolution of an extremum norm problem for the terminal state of a linear system

V. A. Srochko^a, E. V. Aksenyushkina<sup>b

a</sup> Irkutsk State University, Irkutsk, Russian Federation
^b Baikal State University, Irkutsk, Russian Federation

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.

UDC: 517.977

MSC: 49J15, 49M25

Received: 26.10.2020

Language: English

DOI: 10.26516/1997-7670.2020.34.3

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