caa a22 4500 606233393 CHVBK 20210128101232.0 cr unu---uuuuu 210128e20151001xx s 000 0 eng 10.1007/s10883-015-9284-5 doi (NATIONALLICENCE)springer-10.1007/s10883-015-9284-5 Construction of a Set of Restricted Inertial Controls for C(1)-Smooth Affine Systems with Multidimensional Control [Elektronische Daten] [V. Korobov, V. Skoryk] Affine control systems of the class C (1) with multidimensional control are considered. For those systems which can be reduced to linear systems, the inertial synthesis problem is solved, that is, the problem of finding feedback controls satisfying preassigned constraints on a control and its derivatives up to a given order l. The problem of stabilization by use of inertial controls is also solved. The controllability function method is the basis of the investigation. It is shown that each collection f of r nonnegative non-increasing functions which have no less than n 1, ,n r points of decrease ( n 1+ +n r =n), respectively, and satisfy certain conditions generates a family of controllability functions {Θ f,α (x)} and a family of controls {u f,α (x)} which transfer an arbitrary point x 0 from a certain neighborhood of the origin to the origin in some finite time T f,α (x 0) and satisfy given constraints if α≥2l+1. We estimate the time of motion from below and from above. In the limiting case α=∞, the function Θ f (x) is a Lyapunov function and u f (x) solves the stabilization problem and satisfies given constraints. Springer Science+Business Media New York, 2015 C (1)-smooth nonlinear control systems nationallicence Synthesis problem nationallicence Controllability function method nationallicence Stabilization nationallicence Feedback inertial control nationallicence Korobov V. Department of Differential Equations and Control, V. N. Karazin Kharkov National University, Svobody sq. 4, 61022, Kharkov, Ukraine aut Skoryk V. Department of Differential Equations and Control, V. N. Karazin Kharkov National University, Svobody sq. 4, 61022, Kharkov, Ukraine aut Journal of Dynamical and Control Systems Springer US; http://www.springer-ny.com 21/4(2015-10-01), 513-538 1079-2724 21:4<513 2015 21 10883 https://doi.org/10.1007/s10883-015-9284-5 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10883-015-9284-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Korobov V. Department of Differential Equations and Control, V. N. Karazin Kharkov National University, Svobody sq. 4, 61022, Kharkov, Ukraine aut NATIONALLICENCE 700 1- Skoryk V. Department of Differential Equations and Control, V. N. Karazin Kharkov National University, Svobody sq. 4, 61022, Kharkov, Ukraine aut NATIONALLICENCE 773 0- Journal of Dynamical and Control Systems Springer US; http://www.springer-ny.com 21/4(2015-10-01), 513-538 1079-2724 21:4<513 2015 21 10883