Asymptotic Stabilisation of Distributed Port-Hamiltonian Systems by Boundary Energy-Shaping Control. Issue 1 (2015)

• Record Type: Journal Article
• Authors: Macchelli, Alessandro; Gorrec, Yann Le; Ramirez, Héctor
• Is Part Of: IFAC-PapersOnLine. Volume 48:Issue 1(2015)
• Page Start: 488
• Page End: 493
• Publication Date: 2015
• Subjects: distributed port-Hamiltonian systems -- boundary control -- energy-shaping control -- stability of PDEs; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2015.05.143
• Languages: English
• ISSNs: 2405-8963

Abstract

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 the 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.