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R. Kálmán, P. Falb, M. Arbib (1969)
Topics in Mathematical System Theory
Differential Equations, Vol. 40, No. 6, 2004, pp. 789–796. Translated from Differentsial'nye Uravneniya, Vol. 40, No. 6, 2004, pp. 740–746. Original Russian Text Copyright c 2004 by Kvitko. ORDINARY DIFFERENTIAL EQUATIONS A. N. Kvitko St. Petersburg State University, St. Petersburg, Russia Received September 23, 2002 1. INTRODUCTION An algorithm for constructing a control function such that the solution of a linear or quasilinear system of di erential equations passes from the initial state into an arbitrarily small neighborhood of a given terminal state was suggested in [1]. In this paper, we solve a similar problem for a nonlinear control system. Consider the system x _ = f (x;u;t); (1:1) where 1 n n x = x ;:::;x ;x 2 R ; 1 r r u = u ;:::;u ;u 2 R;r n; t 2 [0; 1]; (1:2) 3 n r 1 n f 2 C R R R ;R ;f =(f ;:::;f ) ; 1 n kxk <C : (1:3) In addition, suppose that the second partial derivatives of the right-hand sides of system (1.1) with respect to all components of x, u,and t are bounded for all u 2 R , x, kxk C ,and
Differential Equations – Springer Journals
Published: Nov 14, 2004
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