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.

Macchelli, A., Le Gorrec, Y., Rami­rez, H. (2017). Boundary Energy-Shaping Control of an Ideal Compressible Isentropic Fluid in 1-D. Elsevier B.V. [10.1016/j.ifacol.2017.08.1105].

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

Macchelli, Alessandro
;
2017

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.
2017
IFAC-PapersOnLine
5598
5603
Macchelli, A., Le Gorrec, Y., Rami­rez, H. (2017). Boundary Energy-Shaping Control of an Ideal Compressible Isentropic Fluid in 1-D. Elsevier B.V. [10.1016/j.ifacol.2017.08.1105].
Macchelli, Alessandro; Le Gorrec, Yann; Rami­rez, Hector
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/610350
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