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Communication Dans Un Congrès Année : 2010

On the Use of a Global Control Lyapunov Functional in Infinite-dimensional Predictive Control

Résumé

The paper introduces a Global Control Lyapunov Functional (GCLF) which is an extension of the Lyapunov function proposed by Coron et al. [2007] for linear systems of conservation laws. This function has the advantage in comparison with the one of Coron et al. [2007] that it can deal with all initial conditions. From this, it can be used in the context of the Receding horizon optimal control, and - combined with the approach used by Findensen and Allgower [2002] - to prove that the minimum of the cost function decreases along the corresponding controlled trajectories. Furthermore, by exploiting the argument of Ito and Funisch [2002], it can be proven that this function decreases exponentially. All those results are illustrated by simulations in the case of an open hydraulic channel which is described by Saint-Venant equations. For the simulation, calculus of variations is used to derive the adjoint state of the system and the recently proposed Lattice Boltzmann method (see Zhou [2004], Chopard et al. [2009], Junk and Rheinlainder [2008]) is used to solve both direct and adjoint partial differential equations.
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Dates et versions

hal-00551288 , version 1 (03-01-2011)

Identifiants

  • HAL Id : hal-00551288 , version 1

Citer

van Thang Pham, Didier Georges, Gildas Besancon. On the Use of a Global Control Lyapunov Functional in Infinite-dimensional Predictive Control. SSSC 2010 - 4th IFAC Symposium on System, Structure and Control, Sep 2010, Ancona, Italy. ⟨hal-00551288⟩
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