Approximation theorem for a nonlinear control system with sliding modes |
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Authors: | A V Dmitruk |
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Institution: | (1) Department of Optimal Control, Faculty of Computational Mathematics and Cybernetics, Moscow State University, Leninskie gory, Moscow, 119992, Russia |
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Abstract: | We consider the question of validity of the extension of a nonlinear control system by introducing the so-called sliding modes
(i.e., by convexifying the set of admissible velocities) in the presence of constraints imposed on the endpoints of trajectories.
We prove that a trajectory of the extended system can be approximated by trajectories of the original system if the equality
constraints of the extended system are nondegenerate in the first order. The proof is based on a nonlocal estimate for the
distance to the zero set of the nonlinear operator corresponding to the extended system, and involves a specific iteration
process of corrections.
Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2007, Vol. 256, pp. 102–114. |
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