59 research outputs found
An Adaptive Algorithm for Synchronization in Diffusively Coupled Systems
We present an adaptive algorithm that guarantees synchronization in
diffusively coupled systems. We first consider compartmental systems of ODEs,
where each compartment represents a spatial domain of components interconnected
through diffusion terms with like components in different compartments. Each
set of like components may have its own weighted undirected graph describing
the topology of the interconnection between compartments. The link weights are
updated adaptively according to the magnitude of the difference between
neighboring agents connected by the link. We next consider reaction-diffusion
PDEs with Neumann boundary conditions, and derive an analogous algorithm
guaranteeing spatial homogenization of solutions. We provide a numerical
example demonstrating the results
Conditions for synchronizability in arrays of coupled linear systems
Synchronization control in arrays of identical output-coupled continuous-time
linear systems is studied. Sufficiency of new conditions for the existence of a
synchronizing feedback law are analyzed. It is shown that for neutrally stable
systems that are detectable form their outputs, a linear feedback law exists
under which any number of coupled systems synchronize provided that the
(directed, weighted) graph describing the interconnection is fixed and
connected. An algorithm generating one such feedback law is presented. It is
also shown that for critically unstable systems detectability is not
sufficient, whereas full-state coupling is, for the existence of a linear
feedback law that is synchronizing for all connected coupling configurations
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