3 research outputs found
Robust Consensus for Multi-Agent Systems Communicating over Stochastic Uncertain Networks
In this paper, we study the robust consensus problem for a set of
discrete-time linear agents to coordinate over an uncertain communication
network, which is to achieve consensus against the transmission errors and
noises resulted from the information exchange between the agents. We model the
network by means of communication links subject to multiplicative stochastic
uncertainties, which are susceptible to describing packet dropout, random
delay, and fading phenomena. Different communication topologies, such as
undirected graphs and leader-follower graphs, are considered. We derive
sufficient conditions for robust consensus in the mean square sense. This
results unveil intrinsic constraints on consensus attainment imposed by the
network synchronizability, the unstable agent dynamics, and the channel
uncertainty variances. Consensus protocols are designed based on the state
information transmitted over the uncertain channels, by solving a modified
algebraic Riccati equation.Comment: 9 pages and 3 figures. Submitted to Automatic
Mean sqaure synchronization in large scale nonlinear networks with uncertain links
In this paper, we study the problem of synchronization with stochastic
interaction among network components. The network components dynamics is
nonlinear and modeled in Lure form with linear stochastic interaction among
network components. To study this problem we first prove the stochastic version
of Positive Real Lemma (PRL). The stochastic PRL result is then used to provide
sufficient condition for synchronization of stochastic network system. The
sufficiency condition for synchronization, is a function of nominal (mean)
coupling Laplacian eigenvalues and the statistics of link uncertainty in the
form of coefficient of dispersion (CoD). Contrary to the existing literature on
network synchronization, our results indicate that both the largest and the
second smallest eigenvalue of the mean Laplacian play an important role in
synchronization of stochastic networks. Robust control-based small-gain
interpretation is provided for the derived sufficiency condition which allow us
to define the margin of synchronization. The margin of synchronization is used
to understand the important tradeoff between the component dynamics, network
topology, and uncertainty characteristics. For a special class of network
system connected over torus topology we provide an analytical expression for
the tradeoff between the number of neighbors and the dimension of the torus.
Similarly, by exploiting the identical nature of component dynamics
computationally efficient sufficient condition independent of network size is
provided for general class of network system. Simulation results for network of
coupled oscillators with stochastic link uncertainty are presented to verify
the developed theoretical framework
Performance of Single and Double-Integrator Networks over Directed Graphs
This paper provides a framework to evaluate the performance of single and
double integrator networks over arbitrary directed graphs. Adopting vehicular
network terminology, we consider quadratic performance metrics defined by the
L2-norm of position and velocity based response functions given impulsive
inputs to each vehicle. We exploit the spectral properties of weighted graph
Laplacians and output performance matrices to derive a novel method of
computing the closed-form solutions for this general class of performance
metrics, which include H2-norm based quantities as special cases. We then
explore the effect of the interplay between network properties (e.g. edge
directionality and connectivity) and the control strategy on the overall
network performance. More precisely, for systems whose interconnection is
described by graphs with normal Laplacian L, we characterize the role of
directionality by comparing their performance with that of their undirected
counterparts, represented by the Hermitian part of L. We show that, for
single-integrator networks, directed and undirected graphs perform identically.
However, for double-integrator networks, graph directionality -- expressed by
the eigenvalues of L with nonzero imaginary part -- can significantly degrade
performance. Interestingly in many cases, well-designed feedback can also
exploit directionality to mitigate degradation or even improve the performance
to exceed that of the undirected case. Finally we focus on a system coherence
metric -- aggregate deviation from the state average -- to investigate the
relationship between performance and degree of connectivity, leading to
somewhat surprising findings. For example increasing the number of neighbors on
a \omega-nearest neighbor directed graph does not necessarily improve
performance. Similarly, we demonstrate equivalence in performance between
all-to-one and all-to-all communication graphs.Comment: Index Terms: L2, H2 norm, directed graph, performanc