15,280 research outputs found
Stability Margin Scaling Laws for Distributed Formation Control as a Function of Network Structure
We consider the problem of distributed formation control of a large number of
vehicles. An individual vehicle in the formation is assumed to be a fully
actuated point mass. A distributed control law is examined: the control action
on an individual vehicle depends on (i) its own velocity and (ii) the relative
position measurements with a small subset of vehicles (neighbors) in the
formation. The neighbors are defined according to an information graph.
In this paper we describe a methodology for modeling, analysis, and
distributed control design of such vehicular formations whose information graph
is a D-dimensional lattice. The modeling relies on an approximation based on a
partial differential equation (PDE) that describes the spatio-temporal
evolution of position errors in the formation. The analysis and control design
is based on the PDE model. We deduce asymptotic formulae for the closed-loop
stability margin (absolute value of the real part of the least stable
eigenvalue) of the controlled formation. The stability margin is shown to
approach 0 as the number of vehicles N goes to infinity. The exponent on the
scaling law for the stability margin is influenced by the dimension and the
structure of the information graph. We show that the scaling law can be
improved by employing a higher dimensional information graph.
Apart from analysis, the PDE model is used for a mistuning-based design of
control gains to maximize the stability margin. Mistuning here refers to small
perturbation of control gains from their nominal symmetric values. We show that
the mistuned design can have a significantly better stability margin even with
a small amount of perturbation. The results of the analysis with the PDE model
are corroborated with numerical computation of eigenvalues with the state-space
model of the formation.Comment: This paper is the expanded version of the paper with the same name
which is accepted by the IEEE Transactions on Automatic Control. The final
version is updated on Oct. 12, 201
Control limitations from distributed sensing: theory and Extremely Large Telescope application
We investigate performance bounds for feedback control of distributed plants
where the controller can be centralized (i.e. it has access to measurements
from the whole plant), but sensors only measure differences between neighboring
subsystem outputs. Such "distributed sensing" can be a technological necessity
in applications where system size exceeds accuracy requirements by many orders
of magnitude. We formulate how distributed sensing generally limits feedback
performance robust to measurement noise and to model uncertainty, without
assuming any controller restrictions (among others, no "distributed control"
restriction). A major practical consequence is the necessity to cut down
integral action on some modes. We particularize the results to spatially
invariant systems and finally illustrate implications of our developments for
stabilizing the segmented primary mirror of the European Extremely Large
Telescope.Comment: submitted to Automatic
A Parallel Mesh-Adaptive Framework for Hyperbolic Conservation Laws
We report on the development of a computational framework for the parallel,
mesh-adaptive solution of systems of hyperbolic conservation laws like the
time-dependent Euler equations in compressible gas dynamics or
Magneto-Hydrodynamics (MHD) and similar models in plasma physics. Local mesh
refinement is realized by the recursive bisection of grid blocks along each
spatial dimension, implemented numerical schemes include standard
finite-differences as well as shock-capturing central schemes, both in
connection with Runge-Kutta type integrators. Parallel execution is achieved
through a configurable hybrid of POSIX-multi-threading and MPI-distribution
with dynamic load balancing. One- two- and three-dimensional test computations
for the Euler equations have been carried out and show good parallel scaling
behavior. The Racoon framework is currently used to study the formation of
singularities in plasmas and fluids.Comment: late submissio
Distributed Receding Horizon Control with Application to Multi-Vehicle Formation Stabilization
We consider the control of interacting subsystems whose dynamics and constraints are uncoupled, but whose state vectors are coupled non-separably in a single centralized cost function of a finite horizon optimal control problem. For a given centralized cost structure, we generate distributed optimal control problems for each subsystem and establish that the distributed receding horizon implementation is asymptotically stabilizing. The communication requirements between subsystems with coupling in the cost function are that each subsystem obtain the previous optimal control trajectory of those subsystems at each receding horizon update. The key requirements for stability are that each distributed optimal control not deviate too far from the previous optimal control, and that the receding horizon updates happen sufficiently fast. The theory is applied in simulation for stabilization of a formation of vehicles
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