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Inverse optimal control of evolution systems and its application to extensible and shearable slender beams

Research Square

Research Square

  • First Author :
    K. D. Do
  • Co-authors :
    A. D. Lucey
  • Journal Name :
    IEEE Explore
  • Read Full text :
  • DOI :
    10.1109/JAS.2019.1911381

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Abstract

An optimal (practical) stabilization problem is formulated in an inverse approach and solved for nonlinear evolution systems in Hilbert spaces. The optimal control design ensures global well-posedness and global practical K ∞ -exponential stability of the closed-loop system, minimizes a cost functional, which appropriately penalizes both state and control in the sense that it is positive definite (and radially unbounded) in the state and control, without having to solve a Hamilton-Jacobi-Belman equation (HJBE). The Lyapunov functional used in the control design explicitly solves a family of HJBEs. The results are applied to design inverse optimal boundary stabilization control laws for extensible and shearable slender beams governed by fully nonlinear partial differential equations.

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