Construction of a Set of Restricted Inertial Controls for C-(1)-Smooth Affine Systems with Multidimensional Control

摘要

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),aEuro broken vertical bar,n (r) points of decrease ( n (1)+aEuro broken vertical bar+n (r) =n), respectively, and satisfy certain conditions generates a family of controllability functions {I similar to (f,alpha) (x)} and a family of controls {u (f,alpha) (x)} which transfer an arbitrary point x (0) from a certain neighborhood of the origin to the origin in some finite time T (f,alpha) (x (0)) and satisfy given constraints if alpha a parts per thousand yen2l+1. We estimate the time of motion from below and from above. In the limiting case alpha=a, the function I similar to (f) (x) is a Lyapunov function and u (f) (x) solves the stabilization problem and satisfies given constraints.