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Alexander Fradkov, I. Miroshnik, V. Nikiforov (1999)
Nonlinear and Adaptive Control of Complex Systems
A. Isidori (1985)
Nonlinear Control Systems
ISSN 0012-2661, Differential Equations, 2007, Vol. 43, No. 6, pp. 767–773. c Pleiades Publishing, Ltd., 2007. Original Russian Text c S.B. Tkachev, 2007, published in Differentsial’nye Uravneniya, 2007, Vol. 43, No. 6, pp. 753–759. ORDINARY DIFFERENTIAL EQUATIONS Stabilization of Programmed Motions by the Virtual Output Method S. B. Tkachev Bauman Moscow State Technical University, Moscow, Russia Received November 20, 2006 DOI: 10.1134/S0012266107060043 INTRODUCTION For a smooth affine system n 1 x ˙ = A(x)+ B(x)u, x ∈ R,u ∈ R , T T (1) A(x)=(a (x),... ,a (x)) ,B(x)= (b (x),... ,b (x)) , 1 n 1 n ∞ n a (x),b (x) ∈ C (R ),i =1,... ,n, i i with a scalar control, we consider the problem on the stabilization of a given programmed motion ∗ ∗ (x (t),u (t)), t ≥ 0, for a completely known state vector. For nonlinear systems, one known ap- proach is based on the reduction of system (1) in R to a regular canonical [1, 2] or quasicanonical [3] form. To reduce the system to these forms, one should find a function ϕ(x) whose derivatives along the trajectories of system (1) up to a given order do not contain
Differential Equations – Springer Journals
Published: Jul 23, 2007
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