Advances in Non-Integer Order Calculus and Its Applications

Name: Advances in Non-Integer Order Calculus and Its Applications | Proceedings of the 10th International Conference on Non-Integer Order Calculus and Its Applications
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Proceedings of the 10th International Conference on Non-Integer Order Calculus and Its Applications

Agnieszka B. Malinowska Dorota Mozyrska Lukasz Sajewski(Editor)

Springer (Publisher)

1st Edition

Published on 17. April 2019

XIII, 307 pages

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978-3-030-17344-9 (ISBN)

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Content

Intro
Preface
Organization
Scientific Committee
Chair
Co-chair
Members
Organizing Committee
Chair
Co-chair
Members
Supporting Team
Referees
Sponsoring Institution
Contents
Mathematical Foundations
Extensions of Kharitonov Theorem to Positive Fractional Linear Systems
1 Introduction
2 Problem Formulation
3 Extension of Kharitonov Theorem to Positive Interval Linear Systems
4 Fractional Interval Positive Linear Continuous-Time Systems
5 Polynomials with Interval Coefficients of Fractional Positive Linear systems
6 Fractional Discrete-Time Linear System
7 Fractional Interval Positive Linear Discrete-Time Systems
8 Convex Linear Combination of Schur Polynomials and Stability of Interval Fractional Positive Linear Systems
9 Concluding Remarks
References
An Extension of the Fractional Gronwall Inequality
1 Introduction
2 Preliminaries
3 A Fractional Gronwall Type Inequality
References
The Particular Types of Fractional Variable-Order Symmetric Operators
1 Introduction
2 Fractional Variable Order Grünwald-Letnikov Type Derivatives
3 Symmetric Variable Order Derivatives
4 Numerical Example
5 Conclusions
References
Approximation, Modeling and Simulations
Realization of the Fractional Variable-Order Model with Symmetric Property
1 Introduction
2 Fractional Variable-Order Operators
2.1 Definitions of Variable-Order Operators
2.2 Duality Between Fractional Variable-Order Derivatives
2.3 Symmetric Variable-Order Derivatives
3 The Fractional Order Impedance
3.1 The Constant Phase Element Method (CPE)
3.2 Modification of the CPE Method for Variable-Order Case
4 Fractional Variable-Order Symmetric Operator
5 Numerical Examples
6 Conclusions
References
Using Fractional Calculus in an Attempt at Modeling a High Frequency AC Exciter
1 Introduction
2 Mathematical Description of the Model
3 An Integer Order Model
4 Fractional Order Model Structure
5 Power Plant Test Disturbances
6 Filtering of the Waveforms Obtained from Measurements
7 Assumptions for Computations
8 Computation Results
9 Concluding Remarks
References
Numerical Simulations for Fitting Parameters of Linear and Logistic-Type Fractional-, Variable-Order Equations - Comparision of Methods
1 Introduction
2 Preliminaries
2.1 Linear Equation
2.2 Logistic-Type Equation
3 Data Fitting Algorithms
3.1 Trust Region Method
3.2 Particle Swarm Optimization
3.3 Simulated Annealing Algorithm
3.4 Genetic Algorithm
4 Data Fitting Results
4.1 Preparation of Simulated Experimental Data
4.2 Research Methodology
4.3 Linear Equation Fitting Results
4.4 Logistic-Type Equation Fitting Results
5 Summary
References
Selected Implementation Issues in Computation of the Grünwald-Letnikov Fractional-Order Difference by Means of Embedded System
1 Introduction
2 System Representation
2.1 Fractional-Order Difference
2.2 Fractional-Order System
3 Implementation of the `error free transformations'
4 Simulation Examples
4.1 Example 1
4.2 Example 2
4.3 Example 3
4.4 Example 4
5 Conclusion
References
Fractional Systems Analysis and Control
Complex Dynamics in Basic Two-Component Auto-Oscillation Systems with Fractional Derivatives of Different Orders
1 Introduction
2 Mathematical Model
2.1 General Mathematical Model
2.2 Basic Mathematical Model
3 Linear Stability Analysis
4 Computer Simulation of Stability Domains and Nonlinear Dynamics for Basic Mathematical Models
5 Conclusions
References
Switched Fractional State-Space Predictive Control Methods for Non-Linear Fractional Systems
1 Introduction
2 Nonlinear State-Space Fractional Order Predictive Control
2.1 Fractional-Order Nonlinear State-Space Model
2.2 Nonlinear Fractional-Order Model Predictive Control
2.3 Fractional-Order MPC with Linearization and Nonlinear Free Trajectory
3 Proposed Switched Fractional-Order State-Space MPC
3.1 Switched Models of Fractional-Integer Order Nonlinear Processes
3.2 Switched FOSMPC with Nonlinear Prediction and On-line Linearization (FOSMPC-NPL)
3.3 Switched FOSMPC with Nonlinear Prediction and Linearization Along the Predicted Trajectory (FOSMPC-NPL+)
4 Conclusion
References
Design of an Optimal Input Signal for Parameter Estimation of Linear Fractional-Order Systems
1 Introduction
2 Fractional-Order Optimal Control Problem
3 Non-integer Order Operator Approximation
4 Optimal Input Design Problem Formulation
5 Optimal Input Design for Non-integer LTI System Identification
6 Optimal Inputs - Experimental Results
7 Conclusions
References
Non-Integer Order Control of PMSM Drives with Two Nested Feedback Loops
1 Introduction
2 Statement of the PMSM Control Problem
2.1 PMSM Mathematical Model
2.2 Design of Integer Order PI Controllers
2.3 Design of Fractional Order PI Controllers
3 Simulation Results
4 Conclusions
References
Fractional Cucker-Smale Type Models with the Caputo Variable-Order Operator
1 Introduction
2 Preliminaries
3 Fractional Cucker-Smale Type Models with the Caputo Operators
4 Examples
5 Conclusions
References
Exponential Stability for a Class of Fractional Order Dynamic Systems
1 Motivation
2 Preliminaries
3 The Fractional Order Dynamic System
4 Main Results
5 Example
6 Final Conclusions
References
Aspects of the Finite Step Observability of Fractional Order Discrete-Time Polynomial Systems
1 Introduction
2 Preliminaries
2.1 Algebraic Properties
3 Polynomial System with Fractional Order
4 Indistinguishability Relation
5 Relations Between Different Approaches to q-observability
6 Conclusions
References
Stability Analysis for a Class of Fractional Discrete-Time Linear Scalar Systems with Multiple Delays in State
1 Introduction
2 Problem Formulation
3 Solution of the Problem
3.1 Practical Stability
3.2 Asymptotic Stability
4 Concluding Remarks
References
Inaccuracies Revealed During the Analysis of Propagation of Measurement Uncertainty Through a Closed-Loop Fractional-Order Control System
1 Introduction
2 Metrological Background
3 Fractional-Order Differential Equations
4 Simulation Experiments
4.1 Imperfections in Step Responses
4.2 Drifts
5 Conclusions
References
Applications
A Nonlocal Image Inpainting Problem Using the Linear Allen-Cahn Equation
1 Introduction
1.1 Previous Work
1.2 Current Contribution
2 Numerical Method
2.1 Preliminaries
2.2 Discretization of the Equation
3 Results
4 Conclusion
References
PSO Identification for Discrete Fractional Order Model of Heat Transfer Process
1 Introduction
2 Preliminaries
2.1 Elementary Ideas
3 The Considered Inertial, Hybrid, Fractional Order Transfer Function
4 Parameter Identification Problem and Its PSO-Based Solution
5 Experiments
6 Final Conclusions
References
Frequency Method for Determining the Equivalent Parameters of Fractional-Order Elements LC
1 Introduction
2 Resonance in Fractional-Order Circuit of the Class RLC
3 Method of Identifying Parameters of Fractional-Order Elements
3.1 Determination of Supercapacitor Parameters C,
3.2 Determination of Fractional-Order Inductance Parameters L,
4 Experimental Example
5 Conclusions
References
Time-Fractional Heat Conduction with Heat Absorption in a Half-Line Domain Due to Boundary Value of the Heat Flux Varying Harmonically in Time
1 Introduction
2 Statement and Solution of the Problem
2.1 The Mathematical Neumann Boundary Condition
3 The Physical Neumann Boundary Condition
4 Conclusions
References
Complexity of an Identification Problem of Sharp Local Density Loss in Fractional Body
1 Introduction
2 1D Linear Dynamics in the Framework of s-FCM
2.1 Governing Equation
2.2 Eigenproblem - Approximation Scheme
3 Optimization Complexity - Case Study
3.1 Complexity - General Remarks
3.2 Model
3.3 Optimization Problem
3.4 Complexity Measurement
3.5 Results
4 Conclusions
References
Switching Energy Loss in Fractional-Order Time-Varying Heat Diffusion Model
1 Introduction
2 Variable-Order Definitions
3 Examined Model
4 Numerical Results
5 Further Research
6 Conclusions
References
Author Index

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Advances in Non-Integer Order Calculus and Its Applications

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