Displaying similar documents to “Nonlinear diffusion equations with variable coefficients as gradient flows in Wasserstein spaces”

The steepest descent dynamical system with control. Applications to constrained minimization

Alexandre Cabot (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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Let be a real Hilbert space, Φ 1 : H → a convex function of class 𝒞 1 that we wish to minimize under the convex constraint . A classical approach consists in following the trajectories of the generalized steepest descent system (  Brézis [CITE]) applied to the non-smooth function  Φ 1 + δ S . Following Antipin [1], it is also possible to use a continuous gradient-projection system. We propose here an alternative method as follows: given a smooth convex function  Φ 0 : H → whose critical points coincide with  and...

Controlled functional differential equations: approximate and exact asymptotic tracking with prescribed transient performance

Eugene P. Ryan, Chris J. Sangwin, Philip Townsend (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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A tracking problem is considered in the context of a class 𝒮 of multi-input, multi-output, nonlinear systems modelled by controlled functional differential equations. The class contains, as a prototype, all finite-dimensional, linear, -input, -output, minimum-phase systems with sign-definite “high-frequency gain". The first control objective is tracking of reference signals by the output of any system in 𝒮 : given λ ≥ 0 , construct a feedback strategy which ensures that, for every (assumed...