663 research outputs found
Hybrid Geometric Reduction of Hybrid Systems
This paper presents a unifying framework in
which to carry out the hybrid geometric reduction of hybrid
systems, generalizing classical reduction to a hybrid setting
Nonholonomic motion planning: steering using sinusoids
Methods for steering systems with nonholonomic constraints between arbitrary configurations are investigated. Suboptimal trajectories are derived for systems that are not in canonical form. Systems in which it takes more than one level of bracketing to achieve controllability are considered. The trajectories use sinusoids at integrally related frequencies to achieve motion at a given bracketing level. A class of systems that can be steered using sinusoids (claimed systems) is defined. Conditions under which a class of two-input systems can be converted into this form are given
Nonlinear Compressive Particle Filtering
Many systems for which compressive sensing is used today are dynamical. The
common approach is to neglect the dynamics and see the problem as a sequence of
independent problems. This approach has two disadvantages. Firstly, the
temporal dependency in the state could be used to improve the accuracy of the
state estimates. Secondly, having an estimate for the state and its support
could be used to reduce the computational load of the subsequent step. In the
linear Gaussian setting, compressive sensing was recently combined with the
Kalman filter to mitigate above disadvantages. In the nonlinear dynamical case,
compressive sensing can not be used and, if the state dimension is high, the
particle filter would perform poorly. In this paper we combine one of the most
novel developments in compressive sensing, nonlinear compressive sensing, with
the particle filter. We show that the marriage of the two is essential and that
neither the particle filter or nonlinear compressive sensing alone gives a
satisfying solution.Comment: Accepted to CDC 201
Sufficient conditions for the existence of Zeno behavior in a class of nonlinear hybrid systems via constant approximations
The existence of Zeno behavior in hybrid systems
is related to a certain type of equilibria, termed Zeno equilibria,
that are invariant under the discrete, but not the continuous,
dynamics of a hybrid system. In analogy to the standard
procedure of linearizing a vector field at an equilibrium point to
determine its stability, in this paper we study the local behavior
of a hybrid system near a Zeno equilibrium point by considering
the value of the vector field on each domain at this point, i.e., we
consider constant approximations of nonlinear hybrid systems.
By means of these constant approximations, we are able to
derive conditions that simultaneously imply both the existence
of Zeno behavior and the local exponential stability of a Zeno
equilibrium point. Moreover, since these conditions are in terms
of the value of the vector field on each domain at a point, they
are remarkably easy to verify
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