Fractional-order modeling : of dynamic systems with applications in optimization, signal processing, and control /

Detalles Bibliográficos
Clasificación:Libro Electrónico
Otros Autores: Radwan, Ahmed G. (Editor ), Khanday, Farooq Ahmad (Editor ), Said, Lobna A. (Editor )
Formato: Electrónico eBook
Idioma:Inglés
Publicado: London ; San Diego, CA : Academic Press, [2022]
Colección:Emerging methodologies and applications in modelling, identification and control ; volume 2
Temas:
Intelligent control systems > Mathematical models.
Fractional calculus.
Commande intelligente > Mod�eles math�ematiques.
D�eriv�ees fractionnaires.
Fractional calculus
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Front Cover
  • Fractional-Order Modeling of Dynamic Systems with Applications in Optimization, Signal Processing, and Control
  • Copyright
  • Contents
  • List of contributors
  • 1 Continuous and discrete symmetry methods for fractional differential equations
  • 1.1 Introduction
  • 1.2 Continuous and discrete symmetry for classical differential equations
  • 1.2.1 Continuous symmetry method
  • 1.2.2 Discrete symmetry method
  • 1.3 Continuous symmetry for fractional differential equation
  • 1.3.1 Some basic results on fractional calculus
  • 1.3.2 Continuous symmetry for fractional ordinary differential equations
  • 1.3.3 Continuous symmetry for fractional partial differential equations
  • 1.3.4 Some illustrative examples
  • 1.4 Discrete symmetry for fractional Harry Dym equation
  • 1.5 Conclusion
  • References
  • 2 Some theoretical and computation results about COVID-19 by using a fractional-order mathematical model
  • 2.1 Introduction
  • 2.2 Background materials
  • 2.3 Main work
  • 2.3.1 Qualitative analysis of (2.2)
  • 2.3.2 Qualitative analysis for (2.3)
  • 2.4 Series solution of the considered system (2.2) under normal Caputo derivative
  • 2.4.1 Approximate solution and discussion for (2.2)
  • Case I
  • Case II
  • Case III
  • Case IV
  • Case V
  • 2.5 General series solution of the considered system (2.3)
  • 2.5.1 Numerical results and discussion for (2.3)
  • 2.5.2 Conclusion
  • Declaration of competing interest
  • References
  • 3 Spatial-fractional derivatives for fluid flow and transport phenomena
  • 3.1 Introduction
  • 3.2 Preliminary concepts
  • 3.3 Spatial-fractional mass conservation equation
  • 3.4 Fractional Navier-Stokes equation
  • 3.5 Special cases
  • 3.5.1 Poiseuille flow
  • 3.5.2 Boundary layer flow
  • 3.6 Fractional models of flow in porous media
  • 3.6.1 Fractional Darcy's law with time memory.
  • 3.6.2 Fractional Darcy law with space memory
  • 3.7 Fractional natural gas equation
  • 3.8 Fractional multiphase flows in porous media
  • 3.9 Special cases of two-phase flow
  • 3.9.1 Imbibition flow
  • 3.9.2 Fractional momentum with time memory
  • 3.9.3 Fractional mass equation with time memory
  • 3.9.4 Fractional mass and momentum with time memory
  • 3.9.5 Fractional mass and momentum with space memory
  • 3.10 Fractional convection-diffusion equation
  • 3.10.1 Fractional heat conduction model
  • 3.10.2 Fractional transport equation
  • 3.10.3 Applications in cooling and heating systems
  • 3.11 Conclusion
  • References
  • 4 On the hybrid fractional chaotic systems: a numerical approach
  • 4.1 Introduction
  • 4.2 Preliminaries and notations
  • 4.3 Hybrid fractional chaotic models
  • 4.3.1 A hybrid fractional hyperchaotic finance system
  • 4.3.2 Existence and uniqueness of the solution
  • 4.3.3 Equilibrium points and stability
  • 4.3.4 A hybrid fractional Bloch model with time delay
  • 4.3.5 Existence and uniqueness of the time-delayed fractional solution
  • 4.4 Numerical methods for solving hybrid fractional models
  • 4.4.1 CPC-NSFDM
  • 4.4.2 Stability of CPC-NSFDM
  • 4.5 Numerical simulations
  • 4.6 Conclusions
  • Declaration of competing interest
  • References
  • 5 Iterative processes with fractional derivatives
  • 5.1 Introduction
  • 5.2 Preliminary concepts
  • 5.3 Design and analysis of iterative methods using fractional derivatives
  • 5.4 Numerical analysis of the proposed methods
  • 5.4.1 Dependence on initial estimations
  • 5.5 Concluding remarks
  • Acknowledgments
  • References
  • 6 Design of fractional-order finite-time sliding mode controllers for quadrotor UAVs subjected to disturbances and uncertainties
  • 6.1 Introduction
  • 6.1.1 Motivation and background
  • 6.1.2 Literature review
  • 6.1.3 Contributions
  • 6.1.4 Chapter organization.
  • 6.2 Preliminary results
  • 6.3 Quadrotor system dynamics
  • 6.4 Fractional-order SMC controllers for quadrotors
  • 6.4.1 FOSMC-FOFTSMC design mechanism
  • 6.4.1.1 Translational subsystem controller using FOSMC-FOFTSMC
  • 6.4.1.2 Rotational subsystem controller using FOSMC-FOFTSMC
  • 6.4.2 IFOSMC design structure for UAV systems
  • 6.4.2.1 IFOSMC control for translational systems
  • 6.4.2.2 IFOSMC structure for attitude subsystem
  • 6.5 Simulation results and discussion
  • 6.5.1 Simulation 1
  • 6.5.2 Simulation 2
  • 6.6 Conclusion
  • References
  • 7 Performance evaluation of fractional character vector control applied for doubly fed induction generator operating in a network-connected wind power system
  • 7.1 Introduction
  • 7.2 Variable-speed wind power system modeling
  • 7.2.1 Wind turbine modeling
  • 7.2.2 Dynamic modeling of DFIGs
  • 7.2.3 Maximum power point tracking law
  • 7.3 Vector control scheme of DFIG using fractional-order PI controllers
  • 7.3.1 A brief about fractional calculus
  • 7.3.2 Concept of vector control of DFIG
  • 7.4 Design of FOPI controllers applied in the power and current regulation loops
  • 7.4.1 Design of a fractional-order PI controller as current regulator
  • 7.4.2 Design of a fractional-order PI controller as power regulator
  • 7.5 Numerical results and analysis
  • 7.5.1 Robustness evaluation against generator parameter variations
  • 7.5.2 Robustness evaluation against network voltage drop
  • 7.5.3 Comparative studies
  • 7.6 Conclusion
  • References
  • 8 Finite time synchronization of discontinuous fractional order Cohen-Grossberg memristive neural networks with discrete delays under sliding mode control strategies
  • 8.1 Introduction
  • 8.1.1 Related works
  • 8.2 Preliminaries
  • 8.2.1 Basic tools for fractional-order derivatives
  • 8.2.2 Mittag-Leffler function
  • 8.2.3 Model formulation
  • 8.3 Main results.
  • 8.3.1 Existence of Filippov solutions
  • 8.3.2 Finite time stability criteria for the sliding motion
  • 8.3.3 Reachability criteria
  • 8.4 A numerical example
  • 8.5 Conclusions
  • Acknowledgments
  • References
  • 9 Variable-order control systems: a steady-state error analysis
  • 9.1 Introduction
  • 9.2 Variable-order operators
  • 9.3 Main results
  • 9.4 A method for numerical simulation
  • 9.5 Numerical examples
  • 9.6 Conclusion
  • References
  • 10 Theoretical study in conformal thermal antennas optimized by a fractional energy
  • 10.1 Introduction
  • 10.2 Conformal mapping
  • 10.3 Thermal optimization approach
  • 10.4 CTA optimization
  • 10.4.1 Cylindrical CTA
  • 10.4.2 Quasicylindrical CTA
  • 10.5 Conformal fractional energy
  • 10.6 Conclusion
  • References
  • 11 Optimal design of fractional-order Butterworth filter with improved accuracy and stability margin
  • 11.1 Introduction
  • 11.2 Proposed technique
  • 11.2.1 Determination of optimal coefficients using FPA
  • 11.2.2 Polynomial fitting
  • 11.3 Simulation results and discussion
  • 11.3.1 Design accuracy
  • 11.3.2 Stability margin
  • 11.3.3 Cut-off frequency
  • 11.3.4 Circuit realization
  • 11.4 Conclusions
  • References
  • 12 Pseudospectral methods for the Riesz space-fractional Sch�rdinger equation
  • 12.1 Introduction
  • 12.2 Space-fractional couplers
  • 12.3 Gegenbauer polynomials and their properties
  • 12.4 Numerical schemes
  • 12.4.1 Spatial discretization
  • 12.4.1.1 Nonlinear fractional Riesz space Sch�rdinger equations
  • 12.4.1.2 Coupled nonlinear fractional Riesz space Sch�rdinger equations
  • 12.4.2 Temporal discretization
  • 12.5 Numerical experiments
  • 12.5.1 Convergence test
  • 12.5.2 A single equation
  • 12.5.3 Coupled equations
  • 12.6 Conclusion and discussion
  • References.

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