17 research outputs found
Distributed control design for nonlinear output agreement in convergent systems
This work studies the problem of output agreement in homogeneous networks of nonlinear dynamical systems under time-varying disturbances using controllers placed at the nodes of the networks. For the class of contractive systems, necessary and sufficient conditions for output agreement are derived, and these conditions relate the eigenvalues of the network Laplacian and the node dynamics
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
Cluster synchronization of diffusively-coupled nonlinear systems: A contraction based approach
Finding the conditions that foster synchronization in networked oscillatory
systems is critical to understanding a wide range of biological and mechanical
systems. However, the conditions proved in the literature for synchronization
in nonlinear systems with linear coupling, such as has been used to model
neuronal networks, are in general not strict enough to accurately determine the
system behavior. We leverage contraction theory to derive new sufficient
conditions for cluster synchronization in terms of the network structure, for a
network where the intrinsic nonlinear dynamics of each node may differ. Our
result requires that network connections satisfy a cluster-input-equivalence
condition, and we explore the influence of this requirement on network
dynamics. For application to networks of nodes with neuronal spiking dynamics,
we show that our new sufficient condition is tighter than those found in
previous analyses which used nonsmooth Lyapunov functions. Improving the
analytical conditions for when cluster synchronization will occur based on
network configuration is a significant step toward facilitating understanding
and control of complex oscillatory systems
Reducing the PDEs to ODEs through lie vectors using the integrated factors
We reduce the PDEs to ODEs through Lie vectors as previously done through two reduction stages. Some of these ODEs have no solution. Some researchers in this step, use the SMM, power series method or Riccati equation method to solve non-solvable equations. We use the integrating factors as a tool to reduce the order and the nonlinearity in an ODE. This explores new solutions as it appears for the (2+1)-dimensional (CBS) and (3+1)-dimensional generalized BKP solutions compared results