"Approximation theorem for a nonlinear
control system with sliding modes"

**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) 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.

PDF Text

Russian original:
Аппроксимационная теорема для нелинейной управляемой системы

со скользящими режимами -- Труды МИРАН, т. 256, с. 102—114.