A. Bernoussi (2010)
Mathematical Modelling of Natural Phenomena
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In this work, we present some concepts recently introduced in the analysis and control of distributed parameter systems: , and . These concepts permit to describe many biogeographical phenomena, as those of pollution, desertification or epidemics, which are characterized by a spatio-temporal evolution
Jean-François Couchouron (2011)
ESAIM: Control, Optimisation and Calculus of Variations
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This paper deals with feedback stabilization of second order equations of
the form
Jean-François Couchouron (2011)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
This paper deals with feedback stabilization of second order equations of the form + + = 0, ∈ [0, +∞[, where is a densely defined positive selfadjoint linear operator on a real Hilbert space with compact inverse and is a linear map in diagonal form. It is proved here that the classical sufficient ad-condition of Jurdjevic-Quinn and Ball-Slemrod with the feedback control = ⟨, ...
Marcus Wagner (2011)
ESAIM: Control, Optimisation and Calculus of Variations
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We prove a general relaxation theorem for multidimensional control problems of Dieudonné-Rashevsky type with nonconvex integrands (, , ) in presence of a convex control restriction. The relaxed problem, wherein the integrand has been replaced by its lower semicontinuous quasiconvex envelope with respect to the gradient variable, possesses the same finite minimal value as the original problem, and admits a global minimizer. As an application, we provide existence theorems for the image...
Shun-Jie Li, Witold Respondek (2012)
ESAIM: Control, Optimisation and Calculus of Variations
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We study the problem of flatness of two-input driftless control systems. Although a characterization of flat systems of that class is known, the problems of describing all flat outputs and of calculating them is open and we solve it in the paper. We show that all -flat outputs are parameterized by an arbitrary function of three canonically defined variables. We also construct a system of 1st order PDE’s whose solutions give all -flat...
Shun-Jie Li, Witold Respondek (2012)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
We study the problem of flatness of two-input driftless control systems. Although a characterization of flat systems of that class is known, the problems of describing all flat outputs and of calculating them is open and we solve it in the paper. We show that all -flat outputs are parameterized by an arbitrary function of three canonically defined variables. We also construct a system of 1st order PDE’s whose solutions give all -flat...
Shun-Jie Li, Witold Respondek (2012)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
We study the problem of flatness of two-input driftless control systems. Although a characterization of flat systems of that class is known, the problems of describing all flat outputs and of calculating them is open and we solve it in the paper. We show that all -flat outputs are parameterized by an arbitrary function of three canonically defined variables. We also construct a system of 1st order PDE’s whose solutions give all -flat outputs of two-input driftless systems. We illustrate...