Boundary control of nonlinear distributed parameters port-Hamiltonian models for the shallow water dynamics

Abstract : The port-controlled Hamiltonian formulation for classical hyperbolic systems is first recalled. It is applied to the classical Shallow Water equations used to model the free-surface water dynamics in open-air channels or rivers. Then an “energy shaping” control law suggested by a geometrically reduced mixed finite elements model is derived. It is shown how this control law is independent from the order of the reduced model. A Casimir invariant based energy shaping method for distributed parameter port Hamiltonian systems is developed and used to prove the stability of the desired equilibrium water flow and water levels profiles when the suggested boundary control law is applied directly to the infinite dimensional system.
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Contributor : Eduardo Mendes <>
Submitted on : Friday, June 12, 2009 - 3:51:02 PM
Last modification on : Saturday, April 13, 2019 - 1:34:29 AM

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Alexandru Dimofte, Boussad Hamroun, Laurent Lefèvre, Eduardo Mendes. Boundary control of nonlinear distributed parameters port-Hamiltonian models for the shallow water dynamics. International Review of Automatic Control (IREACO), 2009, 2 (3), pp. 286-299. ⟨hal-00394842⟩

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