175 research outputs found
Reach Control on Simplices by Piecewise Affine Feedback
We study the reach control problem for affine systems on simplices, and the
focus is on cases when it is known that the problem is not solvable by
continuous state feedback. We examine from a geometric viewpoint the structural
properties of the system which make continuous state feedbacks fail. This
structure is encoded by so-called reach control indices, which are defined and
developed in the paper. Based on these indices, we propose a subdivision
algorithm and associated piecewise affine feedback. The method is shown to
solve the reach control problem in all remaining cases, assuming it is solvable
by open-loop controls
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
An hybrid system approach to nonlinear optimal control problems
We consider a nonlinear ordinary differential equation and want to control
its behavior so that it reaches a target by minimizing a cost function. Our
approach is to use hybrid systems to solve this problem: the complex dynamic is
replaced by piecewise affine approximations which allow an analytical
resolution. The sequence of affine models then forms a sequence of states of a
hybrid automaton. Given a sequence of states, we introduce an hybrid
approximation of the nonlinear controllable domain and propose a new algorithm
computing a controllable, piecewise convex approximation. The same way the
nonlinear optimal control problem is replaced by an hybrid piecewise affine
one. Stating a hybrid maximum principle suitable to our hybrid model, we deduce
the global structure of the hybrid optimal control steering the system to the
target
On the Construction of Safe Controllable Regions for Affine Systems with Applications to Robotics
This paper studies the problem of constructing in-block controllable (IBC)
regions for affine systems. That is, we are concerned with constructing regions
in the state space of affine systems such that all the states in the interior
of the region are mutually accessible through the region's interior by applying
uniformly bounded inputs. We first show that existing results for checking
in-block controllability on given polytopic regions cannot be easily extended
to address the question of constructing IBC regions. We then explore the
geometry of the problem to provide a computationally efficient algorithm for
constructing IBC regions. We also prove the soundness of the algorithm. We then
use the proposed algorithm to construct safe speed profiles for different
robotic systems, including fully-actuated robots, ground robots modeled as
unicycles with acceleration limits, and unmanned aerial vehicles (UAVs).
Finally, we present several experimental results on UAVs to verify the
effectiveness of the proposed algorithm. For instance, we use the proposed
algorithm for real-time collision avoidance for UAVs.Comment: 17 pages, 18 figures, under review for publication in Automatic
Online Abstractions for Interconnected Multi-Agent Control Systems
In this report, we aim at the development of an online abstraction framework
for multi-agent systems under coupled constraints. The motion capabilities of
each agent are abstracted through a finite state transition system in order to
capture reachability properties of the coupled multi-agent system over a finite
time horizon in a decentralized manner. In the first part of this work, we
define online abstractions by discretizing an overapproximation of the agents'
reachable sets over the horizon. Then, sufficient conditions relating the
discretization and the agent's dynamics properties are provided, in order to
quantify the transition possibilities of each agent.Comment: 22 pages. arXiv admin note: text overlap with arXiv:1603.0478
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