Reference : A PDE viewpoint on basic properties of coordination algorithms with symmetries
Scientific congresses and symposiums : Paper published in a book
Engineering, computing & technology : Multidisciplinary, general & others
A PDE viewpoint on basic properties of coordination algorithms with symmetries
Sarlette, Alain[Université de Liège - ULg > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Systèmes et modélisation >]
Sepulchre, Rodolphe[Université de Liège - ULg > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Systèmes et modélisation >]
Proceedings of the 48th IEEE Conference on Decision and Control
48th IEEE Conference on Decision and Control
from 15-12-2009 to 18-12-2009
[en] Several recent control applications consider the coordination of subsystems through local interaction. Often the interaction has a symmetry in state space, e.g. invariance with respect to a uniform translation of all subsystem values. The present paper shows that in presence of such symmetry, fundamental properties can be highlighted by viewing the distributed system as the discrete approximation of a partial differential equation. An important fact is that the symmetry on the state space differs from the popular spatial invariance property, which is not necessary for the present results. The relevance of the viewpoint is illustrated on two examples: (i) ill-conditioning of interaction matrices in coordination/consensus problems and (ii) the string instability issue.
Systems and Modeling
This paper presents research results of the Belgian Network DYSCO (Dynamical Systems, Control, and Optimization), funded by the Interuniversity Attraction Poles Program, initiated by the Belgian State, Science Policy Office.