36 research outputs found
Model Reduction Near Periodic Orbits of Hybrid Dynamical Systems
We show that, near periodic orbits, a class of hybrid models can be reduced
to or approximated by smooth continuous-time dynamical systems. Specifically,
near an exponentially stable periodic orbit undergoing isolated transitions in
a hybrid dynamical system, nearby executions generically contract
superexponentially to a constant-dimensional subsystem. Under a non-degeneracy
condition on the rank deficiency of the associated Poincare map, the
contraction occurs in finite time regardless of the stability properties of the
orbit. Hybrid transitions may be removed from the resulting subsystem via a
topological quotient that admits a smooth structure to yield an equivalent
smooth dynamical system. We demonstrate reduction of a high-dimensional
underactuated mechanical model for terrestrial locomotion, assess structural
stability of deadbeat controllers for rhythmic locomotion and manipulation, and
derive a normal form for the stability basin of a hybrid oscillator. These
applications illustrate the utility of our theoretical results for synthesis
and analysis of feedback control laws for rhythmic hybrid behavior
Towards Testable Neuromechanical Control of Architectures for Running
Our objective is to provide experimentalists with neuromechanical control hypotheses that can be tested with kinematic data sets. To illustrate the approach, we select legged animals responding to perturbations during running. In the following sections, we briefly outline our dynamical systems approach, state our over-arching hypotheses, define four neuromechanical control architectures (NCAs) and conclude by proposing a series of perturbation experiments that can begin to identify the simplest architecture that best represents an animal\u27s controller
Dynamical Trajectory Replanning for Uncertain Environments
We propose a dynamical reference generator equipped with an augmented transient “replanning” subsystem that modulates a feedback controller’s efforts to force a mechanical plant to track the reference signal. The replanner alters the reference generator’s output in the face of unanticipated disturbances that drive up the tracking error. We demonstrate that the new reference generator cannot destabilize the tracker, that tracking errors converge in the absence of disturbance, and that the overall coupled reference-tracker system cannot be destabilized by disturbances of bounded energy. We report the results of simulation studies exploring the performance of this new design applied to a two dimensional point mass particle interacting with fixed but unknown terrain obstacles.
For more information: Kod*La
Dimension Reduction Near Periodic Orbits of Hybrid Systems
When the Poincar\'{e} map associated with a periodic orbit of a hybrid
dynamical system has constant-rank iterates, we demonstrate the existence of a
constant-dimensional invariant subsystem near the orbit which attracts all
nearby trajectories in finite time. This result shows that the long-term
behavior of a hybrid model with a large number of degrees-of-freedom may be
governed by a low-dimensional smooth dynamical system. The appearance of such
simplified models enables the translation of analytical tools from smooth
systems-such as Floquet theory-to the hybrid setting and provides a bridge
between the efforts of biologists and engineers studying legged locomotion.Comment: Full version of conference paper appearing in IEEE CDC/ECC 201
Poverty and Food Needs: Sac County, Iowa
Poverty and food insecurity impact the welfare of individuals, families, and communities. This profile describes indicators of poverty, food insecurity, and other measures of general economic well-being in Sac County, Iowa