"Approximation theorem for a nonlinear control system with sliding modes"
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) under 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.
Russian original: Аппроксимационная теорема для нелинейной управляемой системы
со скользящими режимами -- Труды МИРАН, т. 256, с. 102—114.
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