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Improvements on Flat Output Characterization for Fractional Systems

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Published/Copyright: February 10, 2015
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Fractional Calculus and Applied Analysis
From the journal Fractional Calculus and Applied Analysis Volume 18 Issue 1

Abstract

In trajectory planning, flatness is used to compute inputs generating suitable trajectories, without using any integration. The flatness property of linear controllable time-invariant fractional systems is studied. The formalism of polynomial matrix of the fractional differential operator is used leading to the characterization of fractionally flat outputs. The so-called defining matrices, which are transformations that express all system variables in function of the fractionally flat outputs and a finite number of their time derivatives, are introduced and characterized in this fractional context. Flatness of fractional systems is then applied to the trajectory planning of a real thermal experiment.

MSC 2010: 26A33; 34A08; 60G22
Key Words and Phrases: flatness; polynomial matrices; fractional differentiation; fractional systems; fractional flat output; thermal systems; trajectory planning

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Received: 2014-8-26
Published Online: 2015-2-10

© 2015 Diogenes Co., Sofia

Articles in the same Issue

  1. FCAA Related News, Events and Books (FCAA-Volume 18-1-2015)
  2. Electrolytic Fractional Derivative and Integral of Two-Terminal Element
  3. Initial Value Problem of Fractional Integro-Differential Equations in Banach Space
  4. Examples of Analytical Solutions by Means of Mittag-Leffler Function of Fractional Black-Scholes Option Pricing Equation
  5. Multiple Solutions for a Class of Fractional Hamiltonian Systems
  6. Some Analytical and Numerical Properties of the Mittag-Leffler Functions
  7. Sobolev Type Fractional Dynamic Equations and Optimal Multi-Integral Controls with Fractional Nonlocal Conditions
  8. Systems of Nonlinear Fractional Differential Equations
  9. Existence and Multiplicity of Solutions for Nonlinear Elliptic Problems with the Fractional Laplacian
  10. Invariant Subspace Method and Exact Solutions of Certain Nonlinear Time Fractional Partial Differential Equations
  11. Filippov Lemma for a Class of Hadamard-Type Fractional Differential Inclusions
  12. New Stability Results for Partial Fractional Differential Inclusions with Not Instantaneous Impulses
  13. Several Results of Fractional Derivatives in Dʹ(R+)
  14. Modeling Extreme-Event Precursors with the Fractional Diffusion Equation
  15. Multiplicity Results for Integral Boundary Value Problems of Fractional Order with Parametric Dependence
  16. Improvements on Flat Output Characterization for Fractional Systems
  17. Nonlocal Fractional Boundary Value Problems with Slit-Strips Boundary Conditions
  18. Remarks to the Paper “On the Existence of Blow UP Solutions for a Class of Fractional Differential Equations” by Z. Bai et al., In “FCAA”, VOL. 17, NO 4 (2014), 1175-1187
https://doi.org/10.1515/fca-2015-0016
Keywords for this article
flatness; polynomial matrices; fractional differentiation; fractional systems; fractional flat output; thermal systems; trajectory planning

Articles in the same Issue

  1. FCAA Related News, Events and Books (FCAA-Volume 18-1-2015)
  2. Electrolytic Fractional Derivative and Integral of Two-Terminal Element
  3. Initial Value Problem of Fractional Integro-Differential Equations in Banach Space
  4. Examples of Analytical Solutions by Means of Mittag-Leffler Function of Fractional Black-Scholes Option Pricing Equation
  5. Multiple Solutions for a Class of Fractional Hamiltonian Systems
  6. Some Analytical and Numerical Properties of the Mittag-Leffler Functions
  7. Sobolev Type Fractional Dynamic Equations and Optimal Multi-Integral Controls with Fractional Nonlocal Conditions
  8. Systems of Nonlinear Fractional Differential Equations
  9. Existence and Multiplicity of Solutions for Nonlinear Elliptic Problems with the Fractional Laplacian
  10. Invariant Subspace Method and Exact Solutions of Certain Nonlinear Time Fractional Partial Differential Equations
  11. Filippov Lemma for a Class of Hadamard-Type Fractional Differential Inclusions
  12. New Stability Results for Partial Fractional Differential Inclusions with Not Instantaneous Impulses
  13. Several Results of Fractional Derivatives in Dʹ(R+)
  14. Modeling Extreme-Event Precursors with the Fractional Diffusion Equation
  15. Multiplicity Results for Integral Boundary Value Problems of Fractional Order with Parametric Dependence
  16. Improvements on Flat Output Characterization for Fractional Systems
  17. Nonlocal Fractional Boundary Value Problems with Slit-Strips Boundary Conditions
  18. Remarks to the Paper “On the Existence of Blow UP Solutions for a Class of Fractional Differential Equations” by Z. Bai et al., In “FCAA”, VOL. 17, NO 4 (2014), 1175-1187
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