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access icon free sampled-data fuzzy control for non-linear parabolic distributed parameter systems with control inputs missing

  • Author(s): Zi-Peng Wang 1, 2  and  Huai-Ning Wu 1
    • View affiliations
    • Affiliations: 1: Science and Technology on Aircraft Control Laboratory, School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, People's Republic of China ;
      2: School of Electrical Engineering, University of Jinan, Jinan 250022, People's Republic of China
  • Source: Volume 11, Issue 10, 23 June 2017, p. 1530 – 1541
    DOI:  10.1049/iet-cta.2016.0724 , Print ISSN 1751-8644, Online ISSN 1751-8652
© The Institution of Engineering and Technology
Received 16/06/2016, Accepted 11/03/2017, Revised 06/01/2017, Published 16/03/2017

In this study, an sampled-data fuzzy control problem is considered for non-linear parabolic partial differential equation (PPDE) systems with control inputs missing. It is assumed that the actuator to the plant is set to zero if the control inputs missing which occurs in a random way satisfies a Bernoulli distribution. With the aid of the modal decomposition technique, a non-linear ordinary differential equation (ODE) system is initially obtained to represent the dominant dynamics of the PPDE system. Subsequently, a Takagi–Sugeno fuzzy model is utilised to accurately describe the resulting non-linear ODE system. Then, using a novel time-dependent functional and the stochastic analysis technique, an sampled-data fuzzy controller with the stochastic missing data via linear matrix inequalities is proposed to stabilise exponentially the non-linear PPDE system in the mean square sense and achieve an performance for the derived non-linear ODE system. Finally, an example on a temperature cooling fin is given to verify the proposed design strategy.

Inspec keywords: fuzzy control; nonlinear differential equations; asymptotic stability; linear matrix inequalities; stochastic systems; distributed parameter systems; partial differential equations; sampled data systems; H∞ control; nonlinear control systems

Other keywords: time-dependent functional; nonlinear ordinary differential equation system; nonlinear parabolic partial differential equation systems; control input missing; Bernoulli distribution; nonlinear ODE system; stochastic analysis technique; actuator; stochastic missing data; modal decomposition technique; Takagi-Sugeno fuzzy model; H∞ sampled-data fuzzy control; nonlinear parabolic distributed parameter systems; PPDE system; linear matrix inequalities; temperature cooling fin; exponential stability

Subjects: Discrete control systems; Optimal control; Distributed parameter control systems; Mathematical analysis; Time-varying control systems; Algebra; Nonlinear control systems; Fuzzy control; Stability in control theory

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