289 research outputs found
Scalable tube model predictive control of uncertain linear systems using ellipsoidal sets
This work proposes a novel robust model predictive control (MPC) algorithm
for linear systems affected by dynamic model uncertainty and exogenous
disturbances. The uncertainty is modeled using a linear fractional perturbation
structure with a time-varying perturbation matrix, enabling the algorithm to be
applied to a large model class. The MPC controller constructs a state tube as a
sequence of parameterized ellipsoidal sets to bound the state trajectories of
the system. The proposed approach results in a semidefinite program to be
solved online, whose size scales linearly with the order of the system. The
design of the state tube is formulated as an offline optimization problem,
which offers flexibility to impose desirable features such as robust invariance
on the terminal set. This contrasts with most existing tube MPC strategies
using polytopic sets in the state tube, which are difficult to design and whose
complexity grows combinatorially with the system order. The algorithm
guarantees constraint satisfaction, recursive feasibility, and stability of the
closed loop. The advantages of the algorithm are demonstrated using two
simulation studies.Comment: Submitted to International Journal of Robust and Nonlinear Contro
Computationally efficient robust MPC using optimized constraint tightening
A robust model predictive control (MPC) method is presented for linear,
time-invariant systems affected by bounded additive disturbances. The main
contribution is the offline design of a disturbance-affine feedback gain
whereby the resulting constraint tightening is minimized. This is achieved by
formulating the constraint tightening problem as a convex optimization problem
with the feedback term as a variable. The resulting MPC controller has the
computational complexity of nominal MPC, and guarantees recursive feasibility,
stability and constraint satisfaction. The advantages of the proposed approach
compared to existing robust MPC methods are demonstrated using numerical
examples.Comment: Submitted to the 61st IEEE Conference on Decision and Control 202
Radiation from the LTB black hole
Does a dynamical black hole embedded in a cosmological FRW background emit
Hawking radiation where a globally defined event horizon does not exist? What
are the differences to the Schwarzschild black hole? What about the first law
of black hole mechanics? We face these questions using the LTB cosmological
black hole model recently published. Using the Hamilton-Jacobi and radial null
geodesic-methods suitable for dynamical cases, we show that it is the apparent
horizon which contributes to the Hawking radiation and not the event horizon.
The Hawking temperature is calculated using the two different methods giving
the same result. The first law of LTB black hole dynamics and the thermal
character of the radiation is also dealt with.Comment: 9 pages, revised version, Europhysics Letter 2012 97 2900
Do we know the mass of a black hole? Mass of some cosmological black hole models
Using a cosmological black hole model proposed recently, we have calculated
the quasi-local mass of a collapsing structure within a cosmological setting
due to different definitions put forward in the last decades to see how similar
or different they are. It has been shown that the mass within the horizon
follows the familiar Brown-York behavior. It increases, however, outside the
horizon again after a short decrease, in contrast to the Schwarzschild case.
Further away, near the void, outside the collapsed region, and where the
density reaches the background minimum, all the mass definitions roughly
coincide. They differ, however, substantially far from it. Generically, we are
faced with three different Brown-York mass maxima: near the horizon, around the
void between the overdensity region and the background, and another at
cosmological distances corresponding to the cosmological horizon. While the
latter two maxima are always present, the horizon mass maxima is absent before
the onset of the central singularity.Comment: 11 pages, 8 figures, revised version, accepted in General Relativity
and Gravitatio
Mode-coupling theory for multiple-time correlation functions of tagged particle densities and dynamical filters designed for glassy systems
The theoretical framework for higher-order correlation functions involving
multiple times and multiple points in a classical, many-body system developed
by Van Zon and Schofield [Phys. Rev. E 65, 011106 (2002)] is extended here to
include tagged particle densities. Such densities have found an intriguing
application as proposed measures of dynamical heterogeneities in structural
glasses. The theoretical formalism is based upon projection operator techniques
which are used to isolate the slow time evolution of dynamical variables by
expanding the slowly-evolving component of arbitrary variables in an infinite
basis composed of the products of slow variables of the system. The resulting
formally exact mode-coupling expressions for multiple-point and multiple-time
correlation functions are made tractable by applying the so-called N-ordering
method. This theory is used to derive for moderate densities the leading mode
coupling expressions for indicators of relaxation type and domain relaxation,
which use dynamical filters that lead to multiple-time correlations of a tagged
particle density. The mode coupling expressions for higher order correlation
functions are also succesfully tested against simulations of a hard sphere
fluid at relatively low density.Comment: 15 pages, 2 figure
Multiple-Point and Multiple-Time Correlations Functions in a Hard-Sphere Fluid
A recent mode coupling theory of higher-order correlation functions is tested
on a simple hard-sphere fluid system at intermediate densities. Multi-point and
multi-time correlation functions of the densities of conserved variables are
calculated in the hydrodynamic limit and compared to results obtained from
event-based molecular dynamics simulations. It is demonstrated that the mode
coupling theory results are in excellent agreement with the simulation results
provided that dissipative couplings are included in the vertices appearing in
the theory. In contrast, simplified mode coupling theories in which the
densities obey Gaussian statistics neglect important contributions to both the
multi-point and multi-time correlation functions on all time scales.Comment: Second one in a sequence of two (in the first, the formalism was
developed). 12 pages REVTeX. 5 figures (eps). Submitted to Phys.Rev.
Generalized Boltzmann Equation for Lattice Gas Automata
In this paper, for the first time a theory is formulated that predicts
velocity and spatial correlations between occupation numbers that occur in
lattice gas automata violating semi-detailed balance. Starting from a coupled
BBGKY hierarchy for the -particle distribution functions, cluster expansion
techniques are used to derive approximate kinetic equations. In zeroth
approximation the standard nonlinear Boltzmann equation is obtained; the next
approximation yields the ring kinetic equation, similar to that for hard sphere
systems, describing the time evolution of pair correlations. As a quantitative
test we calculate equal time correlation functions in equilibrium for two
models that violate semi-detailed balance. One is a model of interacting random
walkers on a line, the other one is a two-dimensional fluid type model on a
triangular lattice. The numerical predictions agree very well with computer
simulations.Comment: 31 pages LaTeX, 12 uuencoded tar-compressed Encapsulated PostScript
figures (`psfig' macro), hardcopies available on request, 78kb + 52k
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