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The Adjoint Systems of Time Fractional Diffusion Equations and Their Applications in Controllability Analysis

[+] Author Affiliations
Fudong Ge, Chunhai Kou

Donghua University, Shanghai, China

YangQuan Chen

University of California, Merced, CA

Paper No. DETC2015-46696, pp. V009T07A030; 6 pages
doi:10.1115/DETC2015-46696
From:
  • ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 9: 2015 ASME/IEEE International Conference on Mechatronic and Embedded Systems and Applications
  • Boston, Massachusetts, USA, August 2–5, 2015
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5719-9
  • Copyright © 2015 by ASME

abstract

This paper is devoted to the construction of the adjoint system for the case of time fractional order diffusion equations. We first obtain the equivalent integral equation of the abstract fractional state-space system of both Caputo and Riemann-Liouville type by utilizing the Laplace transform and the semigroup theory. Then the adjoint system of time fractional diffusion equation is introduced and used to analyze the duality relationship between observation and control in a Hilbert space. The new introduced notations can also be used in many fields of modelling and control of real dynamic systems.

Copyright © 2015 by ASME

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