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Backstepping control of a hyperbolic PDE system with zero characteristic speed

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  • معلومة اضافية
    • Publisher Information:
      Elsevier 2022
    • نبذة مختصرة :
      In this paper, we study the single-input boundary feedback stabilization of 3 × 3 linear hyperbolic partial differential equations (PDEs) with two counterconvecting PDEs and the third one with zero characteristic speed. We design a full-state backstepping controller which exponentially stabilizes the origin in the L2sense. The zero transport velocity makes the previous backstepping designs inapplicable (their application would result in a controller with infinite gains). To employ backstepping in the presence of zero speed, we use an invertible Volterra transformation only for the PDEs with nonzero speeds, leaving the state of the zero-speed PDE unaltered in the target system, but making the target zero-speed PDE input-to-state stable with respect to the decoupled and stable counterconvecting nonzero-speed PDEs. In addition to achieving stabilization, we produce an explicit bound on the rate of convergence of the target system by a method of successive approximations and the use of Laplace transform. Simulation results are presented to illustrate the effectiveness of the proposed control design.
    • الموضوع:
      Backstepping; Hyperbolic Systems; Linear Control; Partial Differential Equations; Stabilization; Zero Transport Speed; info:eu-repo/semantics/conferenceObject
    • Availability:
      Open access content. Open access content
      http://creativecommons.org/licenses/by-nc-nd/4.0
      info:eu-repo/semantics/openAccess
      Attribution-NonCommercial-NoDerivatives 4.0 Internacional
    • Note:
      English
    • Other Numbers:
      SUE oai:idus.us.es:11441/146837
      Andrade, G.A.d., Vázquez Valenzuela, R., Karafyllis, L. y Krstic, M. (2022). Backstepping control of a hyperbolic PDE system with zero characteristic speed. En 4th IFAC Workshop on Control of Systems Governed by Partial Differential Equations, CPDE 2022, IFAC-PapersOnLine, 55 (26) (168-173).
      2405-8963
      10.1016/j.ifacol.2022.10.395
      1388543302
    • Contributing Source:
      UNIV DE SEVILLA
      From OAIster®, provided by the OCLC Cooperative.
    • الرقم المعرف:
      edsoai.on1388543302
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