402 research outputs found
Modified Gravity and Cosmology
In this review we present a thoroughly comprehensive survey of recent work on
modified theories of gravity and their cosmological consequences. Amongst other
things, we cover General Relativity, Scalar-Tensor, Einstein-Aether, and
Bimetric theories, as well as TeVeS, f(R), general higher-order theories,
Horava-Lifschitz gravity, Galileons, Ghost Condensates, and models of extra
dimensions including Kaluza-Klein, Randall-Sundrum, DGP, and higher
co-dimension braneworlds. We also review attempts to construct a Parameterised
Post-Friedmannian formalism, that can be used to constrain deviations from
General Relativity in cosmology, and that is suitable for comparison with data
on the largest scales. These subjects have been intensively studied over the
past decade, largely motivated by rapid progress in the field of observational
cosmology that now allows, for the first time, precision tests of fundamental
physics on the scale of the observable Universe. The purpose of this review is
to provide a reference tool for researchers and students in cosmology and
gravitational physics, as well as a self-contained, comprehensive and
up-to-date introduction to the subject as a whole.Comment: 312 pages, 15 figure
Robust stability of differential-algebraic equations
This paper presents a survey of recent results on the robust stability analysis and the distance to instability for linear time-invariant and time-varying differential-algebraic equations (DAEs). Different stability concepts such as exponential and asymptotic stability are studied and their robustness is analyzed under general as well as restricted sets of real or complex perturbations. Formulas for the distances are presented whenever these are available and the continuity of the distances in terms of the data is discussed. Some open problems and challenges are indicated
Nonlinear robust H∞ control.
A new theory is proposed for the full-information finite and infinite horizontime
robust H∞ control that is equivalently effective for the regulation and/or tracking
problems of the general class of time-varying nonlinear systems under the presence of
exogenous disturbance inputs. The theory employs the sequence of linear-quadratic and
time-varying approximations, that were recently introduced in the optimal control
framework, to transform the nonlinear H∞ control problem into a sequence of linearquadratic
robust H∞ control problems by using well-known results from the existing
Riccati-based theory of the maturing classical linear robust control. The proposed
method, as in the optimal control case, requires solving an approximating sequence of
Riccati equations (ASRE), to find linear time-varying feedback controllers for such
disturbed nonlinear systems while employing classical methods. Under very mild
conditions of local Lipschitz continuity, these iterative sequences of solutions are
known to converge to the unique viscosity solution of the Hamilton-lacobi-Bellman
partial differential equation of the original nonlinear optimal control problem in the
weak form (Cimen, 2003); and should hold for the robust control problems herein. The
theory is analytically illustrated by directly applying it to some sophisticated nonlinear
dynamical models of practical real-world applications. Under a r -iteration sense, such
a theory gives the control engineer and designer more transparent control requirements
to be incorporated a priori to fine-tune between robustness and optimality needs. It is
believed, however, that the automatic state-regulation robust ASRE feedback control
systems and techniques provided in this thesis yield very effective control actions in
theory, in view of its computational simplicity and its validation by means of classical
numerical techniques, and can straightforwardly be implemented in practice as the
feedback controller is constrained to be linear with respect to its inputs
Born-Infeld inspired modifications of gravity
General Relativity has shown an outstanding observational success in the
scales where it has been directly tested. However, modifications have been
intensively explored in the regimes where it seems either incomplete or signals
its own limit of validity. In particular, the breakdown of unitarity near the
Planck scale strongly suggests that General Relativity needs to be modified at
high energies and quantum gravity effects are expected to be important. This is
related to the existence of spacetime singularities when the solutions of
General Relativity are extrapolated to regimes where curvatures are large. In
this sense, Born-Infeld inspired modifications of gravity have shown an
extraordinary ability to regularise the gravitational dynamics, leading to
non-singular cosmologies and regular black hole spacetimes in a very robust
manner and without resorting to quantum gravity effects. This has boosted the
interest in these theories in applications to stellar structure, compact
objects, inflationary scenarios, cosmological singularities, and black hole and
wormhole physics, among others. We review the motivations, various
formulations, and main results achieved within these theories, including their
observational viability, and provide an overview of current open problems and
future research opportunities.Comment: 212 pages, Review under press at Physics Report
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Optimization methods for deadbeat control design: a state space approach
This thesis addresses the synthesis problem of state deadbeat regulator using state space techniques. Deadbeat control is a linear control strategy in discrete time systems and consists of driving the system from any arbitrary initial state to a desired final state infinite number of time steps.
Having described the framework for development of the thesis which is in the form of a lower linear-fractional transformation (LFT), the conditions for internal stability based on the notion of coprime factorization over the set of proper and stable transfer matrices, namely RH, is discussed. This leads to the derivation of the class of all stabilizing linear controllers, which are parameterized affinely in terms of a stable but otherwise free parameter Q, usually known as the Q-parameterization. In this work, the classical Q- parameterization is generalized to deliver a parameterization for the family of deadbeat regulators.
Time response characteristics of the deadbeat system are investigated. In particular, the deadbeat regulator design problem in which the system must satisfy time domain specifications and minimize a quadratic (LQG-type) performance criterion is examined. It is shown that the attained parameterization for deadbeat controllers leads to the formulation of the synthesis problem in a quadratic programming framework with Q regarded as the design variable. The equivalent formulation of this objective as a quadratic integral in the frequency domain provides the means for shaping the frequency response characteristics of the system. Using the LMI characterization of the standard H problem, a new scheme for shaping the system frequency response characteristics by minimizing the infinity norm of an appropriate closed-loop transfer function is introduced. As shown, the derived parameterization of deadbeat compensators simplifies considerably the formulation and solution of this problem.
The last part of the work described in this thesis is devoted to addressing the synthesis problem of deadbeat regulators in a robust way, when the plant is subject to structured norm-bounded parametric uncertainties. A novel approach which is expressed as an LMI feasibility condition has been proposed and analysed
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