scholarly journals On (h0,h)-stability of autonomous systems

1992 ◽  
Vol 5 (4) ◽  
pp. 331-337 ◽  
Author(s):  
Xinzhi Liu
Keyword(s):  
Asymptotic Stability ◽  
Autonomous System ◽  
Autonomous Systems ◽  
Qualitative Behavior ◽  
Initial Values

In this paper, we discuss the qualitative behavior of a map h along solutions of an autonomous system whose initial values are measured by a second map h0. By doing this, we may deal with, in a unified way, several concepts and associated problems, which are usually considered separately. Five theorems on asymptotic stability are given and two examples are worked out.

TRANSFORMATION TO AUTONOMOUS SYSTEMS VIA HAMILTON’S EQUATIONS

1993 ◽  
Vol 08 (03) ◽  
pp. 233-236
Author(s):  
J.T. ANDERSON
Keyword(s):  
Harmonic Oscillator ◽  
Autonomous System ◽  
Anharmonic Oscillator ◽  
Autonomous Systems ◽  
Time Dependent ◽  
Arbitrary Time ◽  
Initial Values ◽  
Hamilton's Equations ◽  
Hamilton’S Equations

A semiclassical Hamiltonian with arbitrary time-dependent external term is transformed via Hamiltonian’s equations into a time-independent autonomous system. Iteration gives Hamilton’s equations which are functions of the initial values and time-independent external terms. For the harmonic oscillator it is found that no external term gives constants of the motion or semiclassical chaos. A quartic anharmonic oscillator is discussed.

Recursive Lyapunov Functions

1989 ◽  
Vol 111 (4) ◽  
pp. 641-645 ◽  
Author(s):  
Andrzej Olas
Keyword(s):  
Asymptotic Stability ◽  
Lyapunov Function ◽  
Exponential Stability ◽  
Performance Measures ◽  
Lyapunov Functions ◽  
Stability Problem ◽  
Autonomous Systems ◽  
Sequence Of Functions

The paper presents the concept of recursive Lyapunov function. The concept is applied to investigation of asymptotic stability problem of autonomous systems. The sequence of functions {Uα(i)} and corresponding performance measures λ(i) are introduced. It is proven that λ(i+1) ≤ λ(i) and in most cases the inequality is a strong one. This fact leads to a concept of a recursive Lyapunov function. For the very important applications case of exponential stability the procedure is effective under very weak conditions imposed on the function V = U(0). The procedure may be particularly applicable for the systems dependent on parameters, when the Lyapunov function determined from one set of parameters may be employed at the first step of the procedure.

scholarly journals Mathematics of Web science: structure, dynamics and incentives

2013 ◽  
Vol 371 (1987) ◽  
pp. 20120377 ◽  
Author(s):  
Jennifer Chayes
Keyword(s):  
Autonomous System ◽  
World Wide ◽  
Autonomous Systems ◽  
Large Graphs ◽  
Finite Graphs ◽  
Online Networks ◽  
The People ◽  
Web Science ◽  
The World ◽  
Online Experience

Dr Chayes’ talk described how, to a discrete mathematician, ‘all the world’s a graph, and all the people and domains merely vertices’. A graph is represented as a set of vertices V and a set of edges E, so that, for instance, in the World Wide Web, V is the set of pages and E the directed hyperlinks; in a social network, V is the people and E the set of relationships; and in the autonomous system Internet, V is the set of autonomous systems (such as AOL, Yahoo! and MSN) and E the set of connections. This means that mathematics can be used to study the Web (and other large graphs in the online world) in the following way: first, we can model online networks as large finite graphs; second, we can sample pieces of these graphs; third, we can understand and then control processes on these graphs; and fourth, we can develop algorithms for these graphs and apply them to improve the online experience.

scholarly journals On the Global Asymptotic Stability of a Second-Order System of Difference Equations

2008 ◽  
Vol 2008 ◽  
pp. 1-12 ◽  
Author(s):  
Ibrahim Yalcinkaya
Keyword(s):  
Asymptotic Stability ◽  
Difference Equations ◽  
Global Asymptotic Stability ◽  
Second Order ◽  
Order System ◽  
Sufficient Condition ◽  
System Of Difference Equations ◽  
Initial Values

A sufficient condition is obtained for the global asymptotic stability of the following system of difference equations where the parameter and the initial values (for .

scholarly journals A Multi-Dimension Spatial Method for Topology Awareness and Multipath Generating

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 870 ◽  
Author(s):  
Yunchong Guan ◽  
Weimin Lei ◽  
Wei Zhang ◽  
Yuzhuo Zhan ◽  
Hao Li ◽  
...  
Keyword(s):  
Autonomous System ◽  
Overlay Networks ◽  
Autonomous Systems ◽  
Negative Influence ◽  
Spatial Mechanisms ◽  
Multiple Dimensions ◽  
Transmission Quality ◽  
Spatial Method ◽  
Multipath Diversity ◽  
Topology Awareness

Multipath diversity significantly impacts multipath transmission quality. Enough multipath diversity would minimize the negative influence brought by an individual path, thus improving tolerance capability of network congestion and failure. However, multipath diversity is hard to guarantee on overlay networks because of inaccurate awareness of underlay network and multipath generating methods considering little about underlay diversity. In this paper, we design a multi-dimension spatial method for topology awareness and multipath generating. Analyzing that the complicated underlay networks with multiple autonomous systems reduce the accuracy of network positioning for topology awareness, we decompose the underlay networks into multiple dimensions, namely intra and inter autonomous system dimensions. We generate independent views for each autonomous system and merge views by embedding exchange points. Then, we design some spatial mechanisms to evaluate link diversity and to constrain multipath generating. Based on the multi-dimensional view, multipath generating is conducted in inter and intra autonomous system phases. Experiments demonstrate that the proposed method improves topology awareness accuracy and guarantees multipath diversity better and the transmission quality is improved.

An Integral Method of Liapunov Function Generation for Nonlinear Autonomous Systems

1965 ◽  
Vol 32 (3) ◽  
pp. 569-575 ◽  
Author(s):  
J. A. Walker ◽  
L. G. Clark
Keyword(s):  
Asymptotic Stability ◽  
Integral Method ◽  
Autonomous Systems ◽  
Liapunov Function ◽  
Higher Order ◽  
Phase Variable ◽  
Variable Form ◽  
Function Generation ◽  
Liapunov Functions

A method is developed for generating Liapunov functions with which to determine the domain of asymptotic stability for nonlinear autonomous systems of any order, so long as these systems may be represented in phase variable form. The method is illustrated by several examples of higher order.

scholarly journals OCEANIDS: Building Next Generation Maritime Autonomous Systems

2018 ◽  
Author(s):  
M Furlong ◽  
R Marlow ◽  
S McPhail ◽  
A Munafo ◽  
M Pebody ◽  
...  
Keyword(s):  
Long Range ◽  
Autonomous System ◽  
Technological Development ◽  
Autonomous Systems ◽  
Deep Ocean ◽  
Next Generation ◽  
Hazardous Environments ◽  
Long Duration ◽  
Navigational System ◽  
Long Endurance

Oceanids is a 4-year programme for the technological development of innovative Maritime Autonomous System (MAS) platforms and associated sensors that will include next generation robotic AUVs, sensors and networks to undertake ambitious, long-range, long-endurance deployments in extreme and hazardous environments, such as the deep ocean or under-ice environments. This paper describes the design of two new types of robotic AUVs, the Autosub 2000 Under-Ice and the Autosub Long Range 1500 vehicles that are being developed under the programme. Two key components of the AUVs are described, the autonomy framework and the navigational system, which relies on a newly developed terrain-aided navigation (TAN) system. At-sea results of the TAN are also reported as obtained during long duration operational deployments done in 2017. 

scholarly journals Algorithmic Bias in Autonomous Systems

2017 ◽  
Author(s):  
David Danks ◽  
Alex John London
Keyword(s):  
Autonomous System ◽  
Autonomous Systems ◽  
Descriptive Term ◽  
Proper Functioning ◽  
Different Types ◽  
Algorithmic Bias

Algorithms play a key role in the functioning of autonomous systems, and so concerns have periodically been raised about the possibility of algorithmic bias. However, debates in this area have been hampered by different meanings and uses of the term, "bias." It is sometimes used as a purely descriptive term, sometimes as a pejorative term, and such variations can promote confusion and hamper discussions about when and how to respond to algorithmic bias. In this paper, we first provide a taxonomy of different types and sources of algorithmic bias, with a focus on their different impacts on the proper functioning of autonomous systems. We then use this taxonomy to distinguish between algorithmic biases that are neutral or unobjectionable, and those that are problematic in some way and require a response. In some cases, there are technological or algorithmic adjustments that developers can use to compensate for problematic bias. In other cases, however, responses require adjustments by the agent, whether human or autonomous system, who uses the results of the algorithm. There is no "one size fits all" solution to algorithmic bias.

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