1,665,549 research outputs found
Controllability of distributed-parameter systems
Controllability of distributed-parameter control systems is mathematically studied. A general theory for control systems includes those that cannot be described by ordinary differential equations
Equivalence of hybrid dynamical systems
A common theme in theoretical computer science (in particular, the theory of distributed processes and computer-aided verification) and in systems and control theory is to charac-terize systems which are ‘externally equivalent’. The intuitive idea is that we only want to distinguish between two systems if the distinction can be detected by an external syste
Model-Reference Adaptive Control of Distributed Lagrangian Infinite-Dimensional Systems Using Hamiltons Principle
This paper presents a Hamilton's principle for distributed control of infinite-dimensional systems modeled by a distributed form of the Euler-Lagrange method. The distributed systems are governed by a system of linear partial differential equations in space and time. A generalized potential energy expression is developed that can capture most physical systems including those systems that have no spatial distribution. The Hamilton's principle is applied to derive distributed feedback control methods without resorting to the standard weak-form discretization approach to convert an infinite-dimensional systems to a finite-dimensional systems. It can be shown by the principle of least action that the distributed control synthesized by the Hamilton's principle is a minimum-norm control. A model-reference adaptive control framework is developed for distributed Lagrangian systems in the presence of uncertainty. The theory is demonstrated by an application of adaptive flutter suppression control of a flexible aircraft wing
An Algebraic Model For Quorum Systems
Quorum systems are a key mathematical abstraction in distributed
fault-tolerant computing for capturing trust assumptions. A quorum system is a
collection of subsets of all processes, called quorums, with the property that
each pair of quorums have a non-empty intersection. They can be found at the
core of many reliable distributed systems, such as cloud computing platforms,
distributed storage systems and blockchains. In this paper we give a new
interpretation of quorum systems, starting with classical majority-based quorum
systems and extending this to Byzantine quorum systems. We propose an algebraic
representation of the theory underlying quorum systems making use of
multivariate polynomial ideals, incorporating properties of these systems, and
studying their algebraic varieties. To achieve this goal we will exploit
properties of Boolean Groebner bases. The nice nature of Boolean Groebner bases
allows us to avoid part of the combinatorial computations required to check
consistency and availability of quorum systems. Our results provide a novel
approach to test quorum systems properties from both algebraic and algorithmic
perspectives.Comment: 15 pages, 3 algorithm
On wave propagation in inhomogeneous systems
We present a theory of electron, electromagnetic, and elastic wave
propagation in systems consisting of non-overlapping scatterers in a host
medium. The theory provides a framework for a unified description of wave
propagation in three-dimensional periodic structures, finite slabs of layered
structures, and systems with impurities: isolated impurities, impurity
aggregates, or randomly distributed impurities. We point out the similarities
and differences between the different cases considered, and discuss the
numerical implementation of the formalism.Comment: 12 page
Computing fuzzy rough approximations in large scale information systems
Rough set theory is a popular and powerful machine learning tool. It is especially suitable for dealing with information systems that exhibit inconsistencies, i.e. objects that have the same values for the conditional attributes but a different value for the decision attribute. In line with the emerging granular computing paradigm, rough set theory groups objects together based on the indiscernibility of their attribute values. Fuzzy rough set theory extends rough set theory to data with continuous attributes, and detects degrees of inconsistency in the data. Key to this is turning the indiscernibility relation into a gradual relation, acknowledging that objects can be similar to a certain extent. In very large datasets with millions of objects, computing the gradual indiscernibility relation (or in other words, the soft granules) is very demanding, both in terms of runtime and in terms of memory. It is however required for the computation of the lower and upper approximations of concepts in the fuzzy rough set analysis pipeline. Current non-distributed implementations in R are limited by memory capacity. For example, we found that a state of the art non-distributed implementation in R could not handle 30,000 rows and 10 attributes on a node with 62GB of memory. This is clearly insufficient to scale fuzzy rough set analysis to massive datasets. In this paper we present a parallel and distributed solution based on Message Passing Interface (MPI) to compute fuzzy rough approximations in very large information systems. Our results show that our parallel approach scales with problem size to information systems with millions of objects. To the best of our knowledge, no other parallel and distributed solutions have been proposed so far in the literature for this problem
Crux: Locality-Preserving Distributed Services
Distributed systems achieve scalability by distributing load across many
machines, but wide-area deployments can introduce worst-case response latencies
proportional to the network's diameter. Crux is a general framework to build
locality-preserving distributed systems, by transforming an existing scalable
distributed algorithm A into a new locality-preserving algorithm ALP, which
guarantees for any two clients u and v interacting via ALP that their
interactions exhibit worst-case response latencies proportional to the network
latency between u and v. Crux builds on compact-routing theory, but generalizes
these techniques beyond routing applications. Crux provides weak and strong
consistency flavors, and shows latency improvements for localized interactions
in both cases, specifically up to several orders of magnitude for
weakly-consistent Crux (from roughly 900ms to 1ms). We deployed on PlanetLab
locality-preserving versions of a Memcached distributed cache, a Bamboo
distributed hash table, and a Redis publish/subscribe. Our results indicate
that Crux is effective and applicable to a variety of existing distributed
algorithms.Comment: 11 figure
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