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.

Vladimir Srochko, Dr. Sci. (Phys.–Math.), Prof., Irkutsk State University, 1, K. Marks St., Irkutsk, 664003, Russian Federation, tel.: (3952)521276, e-mail: srochko@math.isu.ru

Elena Aksenyushkina, Cand. Sci. (Phys.–Math.), Assoc. Prof., Baikal State University, 11, Lenin St., Irkutsk, 664015, Russian Federation, tel.: (3952)500008, e-mail: aks.ev@mail.ru

Srochko V.A., Aksenyushkina E.V. On Resolution of an Extremum Norm Problem for the Terminal State of a Linear System. The Bulletin of Irkutsk State University. Series Mathematics, 2020, vol. 34, pp. 3-17. https://doi.org/10.26516/1997-7670.2020.34.3

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