Robust output regulation of linear system subject to modeled and unmodeled uncertainty

In this paper, a novel robust output regulation control framework is proposed for the system subject to noise, modeled disturbance and unmodeled disturbance to seek tracking performance and robustness simultaneously. The output regulation scheme is utilized in the framework to track the reference in the presence of modeled disturbance, and the effect of unmodeled disturbance is reduced by an $\mathcal{H}_\infty$ compensator. The Kalman filter can be also introduced in the stabilization loop to deal with the white noise. Furthermore, the tracking error in the presence/absence of noise and disturbance is estimated. The effectiveness and performance of our proposed control framework is verified in the numerical example by applying in the Furuta Inverted Pendulum system

Loop Quantum Cosmology: A Status Report

The goal of this article is to provide an overview of the current state of the art in loop quantum cosmology for three sets of audiences: young researchers interested in entering this area; the quantum gravity community in general; and, cosmologists who wish to apply loop quantum cosmology to probe modifications in the standard paradigm of the early universe. An effort has been made to streamline the material so that, as described at the end of section I, each of these communities can read only the sections they are most interested in, without a loss of continuity.Comment: 138 pages, 15 figures. Invited Topical Review, To appear in Classical and Quantum Gravity. Typos corrected, clarifications and references adde

Some Numerical and Phenomenological Studies in Loop Quantum Cosmology

A key feature of the singularity resolution in loop quantum cosmology (LQC) is the occurrence of the quantum bounce when the spacetime curvature becomes comparable to the Planck scale. The presence of quantum bounce greatly modifies the dynamics of the early universe and can have important implications for observational signatures. Although the quantum bounce has been previously studied via numerical methods for initial conditions that correspond to large macroscopic universes at late times, a detailed study of the robustness of the quantum bounce for a generic class of initial condition has so far been missing due to severe computational challenges. In the first part of this dissertation, we develop the Chimera scheme, an efficient numerical technique, and study the physics of the quantum bounce in an isotropic and homogeneous spacetime. We find that the quantum bounce is a robust phenomenon and independent of initial conditions, while its quantitative features depend on the quantum fluctuations of the initial state. In addition to these results we present a detailed analysis of the validity of the effective description of LQC, which shows that the effective description remains valid so long as the quantum fluctuations in the state are negligible. These results set the stage to compute finer corrections due to the quantum fluctuations of the spacetime geometry to the observational signatures of LQC. Using the Chimera scheme we also study, for the first time, non-singular evolution in the presence of a negative scalar field potential which gives rise to a cyclic universe. In the second part of the thesis, we focus on the phenomenological aspects of the singularity resolution. We study the transitions of various geometrical structures across the bounce and the effect of the quantum bounce on the inflationary scenario in Bianchi-I spacetime. Using the nonsingular evolution of LQC we also explore the possibility of anti-de Sitter to de Sitter vacuum transitions, a long standing problem in the multiverse scenario, which plays an important role in defining a local measure in the multiverse

Is the observable Universe consistent with the cosmological principle?

The cosmological principle (CP)—the notion that the Universe is spatially isotropic and homogeneous on large scales—underlies a century of progress in cosmology. It is conventionally formulated through the Friedmann-Lemaître-Robertson-Walker (FLRW) cosmologies as the spacetime metric, and culminates in the successful and highly predictive Λ-Cold-Dark-Matter (ΛCDM) model. Yet, tensions have emerged within the ΛCDM model, most notably a statistically significant discrepancy in the value of the Hubble constant, H0. Since the notion of cosmic expansion determined by a single parameter is intimately tied to the CP, implications of the H0 tension may extend beyond ΛCDM to the CP itself. This review surveys current observational hints for deviations from the expectations of the CP, highlighting synergies and disagreements that warrant further study. Setting aside the debate about individual large structures, potential deviations from the CP include variations of cosmological parameters on the sky, discrepancies in the cosmic dipoles, and mysterious alignments in quasar polarizations and galaxy spins. While it is possible that a host of observational systematics are impacting results, it is equally plausible that precision cosmology may have outgrown the FLRW paradigm, an extremely pragmatic but non-fundamental symmetry assumption

Progress in Group Field Theory and Related Quantum Gravity Formalisms

Following the fundamental insights from quantum mechanics and general relativity, geometry itself should have a quantum description; the search for a complete understanding of this description is what drives the field of quantum gravity. Group field theory is an ambitious framework in which theories of quantum geometry are formulated, incorporating successful ideas from the fields of matrix models, ten-sor models, spin foam models and loop quantum gravity, as well as from the broader areas of quantum field theory and mathematical physics. This special issue collects recent work in group field theory and these related approaches, as well as other neighbouring fields (e.g., cosmology, quantum information and quantum foundations, statistical physics) to the extent that these are directly relevant to quantum gravity research

Quantum Cosmology

Within the second half of the last century, quantum cosmology concretely became one of the main research lines within gravitational theory and cosmology. Substantial progress has been made. Furthermore, quantum cosmology can become a domain that will gradually develop further over the next handful of decades, perhaps assisted by technological developments. Indications for new physics (i.e., beyond the standard model of particle physics or general relativity) could emerge and then the observable universe would surely be seen from quite a new perspective. This motivates bringing quantum cosmology to more research groups and individuals.This Special Issue (SI) aims to provide a wide set of reviews, ranging from foundational issues to (very) recent advancing discussions. Concretely, we want to inspire new work proposing observational tests, providing an aggregated set of contributions, covering several lines, some of which are thoroughly explored, some allowing progress, and others much unexplored. The aim of this SI is motivate new researchers to employ and further develop quantum cosmology over the forthcoming decades. Textbooks and reviews exist on the present subject, and this SI will complementarily assist in offering open access to a set of wide-ranging reviews. Hopefully, this will assist new interested researchers, in having a single open access online volume, with reviews that can help. In particular, this will help in selecting what to explore, what to read in more detail, where to proceed, and what to investigate further within quantum cosmology

Structure-Preserving Model Reduction of Physical Network Systems

This paper considers physical network systems where the energy storage is naturally associated to the nodes of the graph, while the edges of the graph correspond to static couplings. The first sections deal with the linear case, covering examples such as mass-damper and hydraulic systems, which have a structure that is similar to symmetric consensus dynamics. The last section is concerned with a specific class of nonlinear physical network systems; namely detailed-balanced chemical reaction networks governed by mass action kinetics. In both cases, linear and nonlinear, the structure of the dynamics is similar, and is based on a weighted Laplacian matrix, together with an energy function capturing the energy storage at the nodes. We discuss two methods for structure-preserving model reduction. The first one is clustering; aggregating the nodes of the underlying graph to obtain a reduced graph. The second approach is based on neglecting the energy storage at some of the nodes, and subsequently eliminating those nodes (called Kron reduction).</p