Ukrainian Mathematical Bulletin

Volume 3, Issue 3, 2006 pp. 317-336.

Construction of a Set of Inertial Controls

Authors: Valerij I. Korobov, Vasilij A. Skoryk
Author institution: Vasilij Aleksandrovich Skoryk, Kharkov V. N. Karazin National University, pl. Svobody, 4, 61077, Kharkov, Ukraine, skoryk@univer.kharkov.ua Valerij Ivanovich Korobov, Uniwersytet Szczecinski, Instytut Matematyki, ul. Wielkopolska, 15, Szczecin, Poland; Kharkov V. N. Karazin National University, pl. Svobody, 4, 61077, Kharkov, Ukraine, korobow@sus.univ.szczecin.pl, vkorobov@univer.kharkov.ua

Summary: We consider the problem of an admissible control synthesis for an autonomous system with an $r$-dimensional control subject to restrictions on the control and its derivatives up to a given order $l$. The study is carried out by using a controllability function. First, this problem is solved for a linear system, then for a nonlinear system using its first order approximation in the case $l=1.$ We show that any collection of $r$ functions, each of which is nonnegative, monotone nondecreasing on the nonnegative half-axis and satisfying a certain condition, gives rise to a set of controllability functions and a corresponding set of controls which solve the problem under consideration. The results are illustrated with an example.

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