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Matematicheskaya Fizika, Analiz, Geometriya [Mathematical Physics, Analysis, Geometry], 2001, Volume 8, Number 2, Pages 189–204
(Mi jmag339)
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This article is cited in 2 scientific papers (total in 2 papers)
The continuous dependence of the solution of the controllability problem on the initial and the terminal states for the triangular nonlinearizable systems
V. I. Korobov, S. S. Pavlichkov V. N. Karazin Kharkiv National University, Faculty of Mathematics and Mechanics
Abstract:
Sufficient conditions for the existence of a family of controls $u_{(x^0, x^T)}(\cdot)$, steering the state $x^0 \in{\mathbf R}^n$ into the state $x^T\in{\mathbf R}^n$, for all $x^0\in{\mathbf R}^n$ and $x^T\in{\mathbf R}^n$, and continuously depending on $x^0\in{\mathbf R}^n$ and $x^T\in{\mathbf R}^n$, are given for a class of triangular systems whose trajectories, in general, can not be mapped by a diffeomorphism onto the trajectories of a linear canonical system. As a corollary, the complete controllability of the uniformly bounded perturbations of this class is obtained under the global Lipschitz condition for the right-hand side with respect to $x$ and $u$.
Received: 27.12.2000
Citation:
V. I. Korobov, S. S. Pavlichkov, “The continuous dependence of the solution of the controllability problem on the initial and the terminal states for the triangular nonlinearizable systems”, Mat. Fiz. Anal. Geom., 8:2 (2001), 189–204
Linking options:
https://www.mathnet.ru/eng/jmag339 https://www.mathnet.ru/eng/jmag/v8/i2/p189
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