Boundary Energy-Shaping Control of an Ideal Compressible Isentropic Fluid in 1-D

Authors

Alessandro Macchelli, Yann Le Gorrec, Héctor Ramírez

Abstract

This paper illustrates a synthesis methodology of asymptotically stabilising, energy-based, boundary control laws for a large class of distributed port-Hamiltonian systems. The result is applied on a non-linear model of an ideal, compressible, isentropic fluid with one-dimensional spatial domain. The idea is to design at first a state feedback law able to perform the energy-shaping task, i.e. able to render the closed-loop system a port-Hamiltonian system with a new Hamiltonian with a minimum at the desired equilibrium. Then, under some assumptions on the existence of solutions and pre-compactness of trajectories, asymptotic stability is obtained via damping injection on the boundary. The result is a consequence of the La Salles Invariance Principle in infinite dimensions.

Keywords

distributed port-Hamiltonian systems; ideal compressible isentropic fluid; boundary control; energy-shaping control; stability of PDEs

Citation

• Journal: IFAC-PapersOnLine
• Year: 2017
• Volume: 50
• Issue: 1
• Pages: 5598–5603
• Publisher: Elsevier BV
• DOI: 10.1016/j.ifacol.2017.08.1105
• Note: 20th IFAC World Congress

BibTeX

@article{Macchelli_2017,
  title={{Boundary Energy-Shaping Control of an Ideal Compressible Isentropic Fluid in 1-D}},
  volume={50},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2017.08.1105},
  number={1},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Macchelli, Alessandro and Le Gorrec, Yann and Ramírez, Héctor},
  year={2017},
  pages={5598--5603}
}

Download the bib file

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