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Paraconvex functions and paraconvex sets

Huynh Van Ngai, Jean-Paul Penot (2008)

Studia Mathematica

We study a class of functions which contains both convex functions and differentiable functions whose derivatives are locally Lipschitzian or Hölderian. This class is a subclass of the class of approximately convex functions. It enjoys refined properties. We also introduce a class of sets whose associated distance functions are of that type. We discuss the properties of the metric projections on such sets under some assumptions on the geometry of the Banach spaces in which they are embedded. We...

Parametrization and geometric analysis of coordination controllers for multi-agent systems

Xiaoli Wang, Yiguang Hong (2009)

Kybernetika

In this paper, we address distributed control structures for multi-agent systems with linear controlled agent dynamics. We consider the parametrization and related geometric structures of the coordination controllers for multi-agent systems with fixed topologies. Necessary and sufficient conditions to characterize stabilizing consensus controllers are obtained. Then we consider the consensus for the multi-agent systems with switching interaction topologies based on control parametrization.

Partial regularity for anisotropic functionals of higher order

Menita Carozza, Antonia Passarelli di Napoli (2007)

ESAIM: Control, Optimisation and Calculus of Variations


We prove a C k , α partial regularity result for local minimizers of variational integrals of the type I ( u ) = Ω f ( D k u ( x ) ) d x , assuming that the integrand f satisfies (p,q) growth conditions.


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