8,236 research outputs found
Synthesis for Constrained Nonlinear Systems using Hybridization and Robust Controllers on Simplices
In this paper, we propose an approach to controller synthesis for a class of
constrained nonlinear systems. It is based on the use of a hybridization, that
is a hybrid abstraction of the nonlinear dynamics. This abstraction is defined
on a triangulation of the state-space where on each simplex of the
triangulation, the nonlinear dynamics is conservatively approximated by an
affine system subject to disturbances. Except for the disturbances, this
hybridization can be seen as a piecewise affine hybrid system on simplices for
which appealing control synthesis techniques have been developed in the past
decade. We extend these techniques to handle systems subject to disturbances by
synthesizing and coordinating local robust affine controllers defined on the
simplices of the triangulation. We show that the resulting hybrid controller
can be used to control successfully the original constrained nonlinear system.
Our approach, though conservative, can be fully automated and is
computationally tractable. To show its effectiveness in practical applications,
we apply our method to control a pendulum mounted on a cart
Motion Planning for Kinematic systems
In this paper, we present a general theory of motion planning for kinematic
systems. This theory has been developed for long by one of the authors in a
previous series of papers. It is mostly based upon concepts from subriemannian
geometry. Here, we summarize the results of the theory, and we improve on, by
developping in details an intricated case: the ball with a trailer, which
corresponds to a distribution with flag of type 2,3,5,6.
This paper is dedicated to Bernard Bonnard for his 60th birthday
- …