Non-Integer Order Calculus and its Applications

Name: Non-Integer Order Calculus and its Applications | 9th International Conference on Non-Integer Order Calculus and Its Applications, Lódz, Poland
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Price: 149.79 EUR
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9th International Conference on Non-Integer Order Calculus and Its Applications, Lódz, Poland

Piotr Ostalczyk Dominik Sankowski Jacek Nowakowski(Herausgeber*in)

Springer (Verlag)

Erschienen am 22. März 2018

X, 229 Seiten

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978-3-319-78458-8 (ISBN)

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Beschreibung

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Inhalt

Intro
Preface
Organization
International Program Committee
Conference Chair
Conference Co-chair
Local Organizing Committee
Local Chair
Members
Referees
Supporting Institutions
Contents
Mathematical Foundations
Decentralized Stabilization of Fractional Positive Descriptor Discrete-Time Linear Systems
1 Introduction - New
2 Fractional Descriptor Linear Systems
3 Decentralized Stabilization of Fractional Descriptor Linear Systems
4 Procedure and Illustrating Example
5 Concluding Remarks
References
Non-invasive Control of the Fractional Hegselmann-Krause Type Model
1 Introduction
2 Preliminaries
3 Optimal Control of the Fractional Hegselmann-Krause Type Model with Leadership
3.1 Existence of Solutions
3.2 Necessary Optimality Conditions
4 Illustrative Examples
References
Differintegarator Based on Fractional Calculus of Convex Functions
1 Introduction
2 Differintegator
2.1 System
2.2 Simulation Results
3 Conclusions
References
The AQM Dropping Packet Probability Function Based on Non-integer Order PID Controller
1 Introduction
2 Fractional Calculus
3 The Packet Dropping Probability Function Based on PID Controller
4 Summary
References
New Numerical Techniques for Solving Fractional Partial Differential Equations in Conformable Sense
1 Introduction
2 Some Basic Motivations
3 Adomian Decomposition Method in Conformable Sense
4 Modified Homotopy Perturbation Method in Conformable Sense
5 Applications and Results
5.1 Example
5.2 Example
5.3 Example
6 Concluding Remarks
References
Implementation of Low-Pass Fractional Filtering for the Purpose of Analysis of Electroencephalographic Signals
1 Introduction
2 Electroencephalography - Fundamentals
3 Literature Review
4 Non-integer Filtering
5 Research Methodology
5.1 Conducted Experiments
5.2 Applied Filters
5.3 Oustaloup Approximation Parameters
6 Results
7 Conclusions and Further Research
References
Grünwald-Letnikov-Laguerre Modeling of Discrete-Time Noncommensurate Fractional-Order State Space LTI MIMO Systems
1 Introduction
2 Fractional Difference and Finite Fractional Difference
3 Laguerre-Based Fractional Differences and Their Approximations
4 Unified Framework for FFLD-Based Models of Multivariable Noncommensurate FD
5 Application to Noncommensurate Fractional Order State Space MIMO Systems
5.1 Unified Framework for Fractional Noncommensurate State Space Models
5.2 Implementation of State Space Models
6 Simulation Example
7 Conclusion
References
Stability Analysis of Fractional Discrete-Time Linear Scalar Systems with Pure Delay
Abstract
1 Introduction
2 Problem Formulation
3 Solution of the Problem
4 Concluding Remarks
Acknowledgement
References
Duality Properties of Variable-Type and -Order Differences
1 Introduction
2 Fractional Constant-Type Variable-Order Differences
2.1 Duality Between Fractional Variable-Order Differences
3 Fractional Variable-Type and -Order Differences
3.1 Switching Strategies for Variable-Type and -Order Differences
4 Duality of Variable-Type and -Order Differences-Main Result
5 Numerical Results
6 Conclusion
References
A PLC Implementation of PSE Approximant for Fractional Order Operator
1 An Introduction
2 Preliminaries
2.1 Elementary Ideas
3 The Experimental System
3.1 General Remarks About Implementation of Special Control Algorithms at PLC Platform
3.2 The Hardware
3.3 The Software
4 Experimental Results
References
Memory-Effective Modifications of PSE Approximation
1 Introduction
2 Preliminaries
3 Main Results
4 Numerical Tests
5 Conclusions
References
Comparison Fixed-Point and Floating-Point Implementation of Noninteger Filter of STM Microcontroller
1 Introduction
2 Implementation Non-integer System in Digital Environment
2.1 Oustaloup Approximation
2.2 Time Domain Approximation
2.3 Hardware Realization
3 Experiment
4 Conclusion
References
Fractional Derivative Approach in Modeling of a Nonlinear Coil for Ferroresonance Analyses
1 Introduction
2 Ferroresonance Analysis - State of the Art
2.1 Ferroresonant Modes
2.2 Analysis Tools
3 Considered Ferroresonance Circuit
3.1 Classical Model
3.2 Fractional Model
4 The Test Circuit and Performed Measurements
5 Computation Results
6 Concluding Remarks
References
Modeling
An Extended Kalman Filter for Time Delays Inspired by a Fractional Order Model
1 Introduction
2 Motivation
3 Modelling
4 EKF Using a First Order Time Delay Model
4.1 EKF Using a Fractional Order Time Delay Models
5 Results
6 Conclusions
References
Fractional Linear Systems with Memory Deficiency and Their State-Space Integer-Order Approximation
1 Introduction
2 Fractional Dynamic Models
2.1 Differential (Difference) Calculus of Non-integer Order
2.2 Continuous-Time Dynamic Models of Fractional Order
2.3 Discrete-Time Dynamic Models of Fractional Order
3 Dynamic Models of Fractional Order with Memory Deficiency
3.1 Switched Derivative of Fractional Order with Memory Impairment
3.2 Switched Difference of Fractional Order with Memory Impairment
3.3 Continuous-Time Models of Fractional Order with Memory Deficiency
3.4 Discrete-Time Models of Fractional Order with Memory Deficiency
4 Approximation of Discrete-Time Fractional Linear Systems with Memory Deficiency
4.1 State-Space Integer-Order Approximation
4.2 Reduced Integer-Order Approximation
5 Numerical Examples
6 Summary
References
Fractional Order System Analysis
Analysis of Fractional Electrical Circuit Using Caputo and Conformable Derivative Definitions
1 Introduction
2 Fractional State-Space Equations
3 Fractional Electrical Circuit and Its State-Space Equation
4 Analysis of the Solutions for Caputo Definition
4.1 Initial Response for Caputo Definition
4.2 Forced Response for Caputo Definition
4.3 General Solution
5 Analysis of the Solutions for CFD Definition
5.1 Initial Response for CFD Definition
5.2 Forced Response for CFD Definition
5.3 General Response
6 Numerical Analysis
7 Final Conclusions
References
Application of Fractional-Order Controller
1 Introduction
1.1 Classic Controllers
1.2 Fractional Order Controllers
2 Methods of Approximation of the Transfer Function
2.1 Taylor Polynomial
2.2 Oustaloup Recursive Approximation (ORA)
3 Model of Inverted Pendulum
4 Simulations
5 Verification of the Controllers
6 Conclusion
References
State Delays Extraction in the Fractional-Order State-Space Model
1 Introduction
2 Mathematical Preliminaries
3 Linear Fractional-Order System Description I
4 Numerical Example
5 Linear Fractional-Order System Description II
5.1 Stability Conditions of Linear Fractional-Order System II
6 Numerical Example
7 Concluding Remarks
References
Solutions of Circuits with Fractional, Nonlinear Elements by Means of a SubIval Solver
1 Introduction
2 Application of SubIval
3 Considered Class of Problems
4 Implicit Time Stepping Solver
5 Computational Example
6 Verification of the Results
7 Summary and Conclusions
A Formulation of State Equations
References
Author Index

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