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Nonlinear control of the viscous burgers equation / Krstic, Miroslav in Transactions of the ASME . Journal of dynamic systems, measurement, and control, Vol. 131 N°2 (Mars/Avril 2009) 

Public ISBD [article]  in Transactions of the ASME . Journal of dynamic systems, measurement, and control > Vol. 131 N°2 (Mars/Avril 2009) . - 8 p. Titre : Nonlinear control of the viscous burgers equation : trajectory generation, tracking, and observer design Type de document : texte imprimé Auteurs : Krstic, Miroslav, Auteur ; Lionel Magnis, Auteur ; Vazquez, Rafael, Auteur Année de publication : 2009 Article en page(s) : 8 p. Note générale : dynamic systems Langues : Anglais (eng) Mots-clés : trajectories  (physics);  design;  equations;  feedback Résumé : In a companion paper we have solved the basic problem of full-state stabilization of unstable “shock-like” equilibrium profiles of the viscous Burgers equation with actuation at the boundaries. In this paper we consider several advanced problems for this nonlinear partial differential equation (PDE) system. We start with the problems of trajectory generation and tracking. Our algorithm is applicable to a large class of functions of time as reference trajectories of the boundary output, though we focus in more detail on the special case of sinusoidal references. Since the Burgers equation is not globally controllable, the reference amplitudes cannot be arbitrarily large. We provide a sufficient condition that characterizes the allowable amplitudes and frequencies, under which the state trajectory is bounded and tracking is achieved. We then consider the problem of output feedback stabilization. We design a nonlinear observer for the Burgers equation that employs only boundary sensing. We employ its state estimates in an output feedback control law, which we prove to be locally stabilizing. The output feedback law is illustrated with numerical simulations of the closed-loop system. DEWEY : 629.8 ISSN : 0022-0434 En ligne : http://dynamicsystems.asmedigitalcollection.asme.org/issue.aspx?journalid=117&is [...] [article] Nonlinear control of the viscous burgers equation : trajectory generation, tracking, and observer design [texte imprimé] / Krstic, Miroslav, Auteur ; Lionel Magnis, Auteur ; Vazquez, Rafael, Auteur . - 2009 . - 8 p. dynamic systems Langues : Anglais (eng) in Transactions of the ASME . Journal of dynamic systems, measurement, and control > Vol. 131 N°2 (Mars/Avril 2009) . - 8 p. Mots-clés : trajectories  (physics);  design;  equations;  feedback Résumé : In a companion paper we have solved the basic problem of full-state stabilization of unstable “shock-like” equilibrium profiles of the viscous Burgers equation with actuation at the boundaries. In this paper we consider several advanced problems for this nonlinear partial differential equation (PDE) system. We start with the problems of trajectory generation and tracking. Our algorithm is applicable to a large class of functions of time as reference trajectories of the boundary output, though we focus in more detail on the special case of sinusoidal references. Since the Burgers equation is not globally controllable, the reference amplitudes cannot be arbitrarily large. We provide a sufficient condition that characterizes the allowable amplitudes and frequencies, under which the state trajectory is bounded and tracking is achieved. We then consider the problem of output feedback stabilization. We design a nonlinear observer for the Burgers equation that employs only boundary sensing. We employ its state estimates in an output feedback control law, which we prove to be locally stabilizing. The output feedback law is illustrated with numerical simulations of the closed-loop system. DEWEY : 629.8 ISSN : 0022-0434 En ligne : http://dynamicsystems.asmedigitalcollection.asme.org/issue.aspx?journalid=117&is [...]