This paper illustrates a general synthesis methodology of asymptotic stabilising, energy-based, boundary control laws, that is applicable to a large class of distributed port-Hamiltonian systems. Similarly to the finite dimensional case, the idea is to design a state feedback law able to perform the energy-shaping task, i.e. able to map the open-loop port-Hamiltonian system into a new one in the same form, but characterised by a new Hamiltonian with a unique and isolated minimum at equilibrium. Asymptotic stability is then obtained via damping injection on the boundary, and is a consequence of the La Salle's Invariance Principle in infinite dimensions. The general theory is illustrated with the help of a simple concluding example, i.e. The boundary stabilisation of a transmission line with distributed dissipation.

Macchelli, A., Le Gorrec, Y., Ramírez, H. (2015). Asymptotic stabilisation of distributed port-hamiltonian systems by boundary energy-shaping control [10.1016/j.ifacol.2015.05.143].

Asymptotic stabilisation of distributed port-hamiltonian systems by boundary energy-shaping control

MACCHELLI, ALESSANDRO;
2015

Abstract

This paper illustrates a general synthesis methodology of asymptotic stabilising, energy-based, boundary control laws, that is applicable to a large class of distributed port-Hamiltonian systems. Similarly to the finite dimensional case, the idea is to design a state feedback law able to perform the energy-shaping task, i.e. able to map the open-loop port-Hamiltonian system into a new one in the same form, but characterised by a new Hamiltonian with a unique and isolated minimum at equilibrium. Asymptotic stability is then obtained via damping injection on the boundary, and is a consequence of the La Salle's Invariance Principle in infinite dimensions. The general theory is illustrated with the help of a simple concluding example, i.e. The boundary stabilisation of a transmission line with distributed dissipation.
2015
IFAC Proceedings Volumes (IFAC-PapersOnline)
488
493
Macchelli, A., Le Gorrec, Y., Ramírez, H. (2015). Asymptotic stabilisation of distributed port-hamiltonian systems by boundary energy-shaping control [10.1016/j.ifacol.2015.05.143].
Macchelli, Alessandro; Le Gorrec, Yann; Ramírez, Héctor
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/550718
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