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.
Asymptotic stabilisation of distributed port-hamiltonian systems by boundary energy-shaping control / Macchelli, Alessandro; Le Gorrec, Yann; Ramírez, Héctor. - STAMPA. - 48:1(2015), pp. 488-493. (Intervento presentato al convegno 8th Vienna International Conference on Mathematical Modelling, MATHMOD 2015 tenutosi a Vienna nel 2015) [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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.