1 research outputs found
A Lyapunov Approach to Barrier-Function Based Time-Varying Gains Higher Order Sliding Mode Controllers
In this paper, we present Lyapunov-based {\color{black}time varying}
controllers for {\color{black}fast} stabilization of a perturbed chain of
integrators with bounded uncertainties. We refer to such controllers as
{\color{black}time varying} higher order sliding mode controllers since they
are designed for nonlinear Single-Input-Single-Output (SISO) systems with
bounded uncertainties such that the uncertainty bounds are unknown.
%{\color{blue} OLD: Our main result states that, given any neighborhood
of the origin, we determine a controller insuring, for every
uncertainty bounds, that every trajectory of the corresponding closed loop
system enters and eventually remains there. Furthermore, based on
the homogeneity property, a new asymptotic accuracy, which depends on the size
of , is presented.} We provide a time varying control feedback law
insuring verifying the following: there exists a family of
time varying open sets decreasing to the origin as tends to infinity, such
that, for any unknown uncertainty bounds and trajectory of the
corresponding system, there exists a positive positve for which
and for . %enters convergence in
finite time of all the trajectories to a time varying domain shrinking
to the origin and their maintenance there. Hence, since the function
tends to zero, this leads the asymptotic convergence of all the trajectories to
zero. The effectiveness of these controllers is illustrated through
simulations.Comment: arXiv admin note: text overlap with arXiv:1607.0276