3,462 research outputs found
Consensus with Output Saturations
This paper consider a standard consensus algorithm under output saturations.
In the presence of output saturations, global consensus can not be realized due
to the existence of stable, unachievable equilibrium points for the consensus.
Therefore, this paper investigates necessary and sufficient initial conditions
for the achievement of consensus, that is an exact domain of attraction.
Specifically, this paper considers singe-integrator agents with both fixed and
time-varying undirected graphs, as well as double-integrator agents with fixed
undirected graph. Then, we derive that the consensus will be achieved if and
only if the average of the initial states (only velocities for
double-integrator agents with homogeneous saturation levels for the outputs) is
within the minimum saturation level. An extension to the case of fixed directed
graph is also provided in which an weighted average is required to be within
the minimum saturation limit
r-Robustness and (r,s)-Robustness of Circulant Graphs
There has been recent growing interest in graph theoretical properties known
as r- and (r,s)-robustness. These properties serve as sufficient conditions
guaranteeing the success of certain consensus algorithms in networks with
misbehaving agents present. Due to the complexity of determining the robustness
for an arbitrary graph, several methods have previously been proposed for
identifying the robustness of specific classes of graphs or constructing graphs
with specified robustness levels. The majority of such approaches have focused
on undirected graphs. In this paper we identify a class of scalable directed
graphs whose edge set is determined by a parameter k and prove that the
robustness of these graphs is also determined by k. We support our results
through computer simulations.Comment: 6 pages, 6 figures. Accepted to 2017 IEEE CD
Resilient Leader-Follower Consensus to Arbitrary Reference Values
The problem of consensus in the presence of misbehaving agents has
increasingly attracted attention in the literature. Prior results have
established algorithms and graph structures for multi-agent networks which
guarantee the consensus of normally behaving agents in the presence of a
bounded number of misbehaving agents. The final consensus value is guaranteed
to fall within the convex hull of initial agent states. However, the problem of
consensus tracking considers consensus to arbitrary reference values which may
not lie within such bounds. Conditions for consensus tracking in the presence
of misbehaving agents has not been fully studied. This paper presents
conditions for a network of agents using the W-MSR algorithm to achieve this
objective.Comment: Accepted for the 2018 American Control Conferenc
From Global Linear Computations to Local Interaction Rules
A network of locally interacting agents can be thought of as performing a
distributed computation. But not all computations can be faithfully
distributed. This paper investigates which global, linear transformations can
be computed using local rules, i.e., rules which rely solely on information
from adjacent nodes in a network. The main result states that a linear
transformation is computable in finite time using local rules if and only if
the transformation has positive determinant. An optimal control problem is
solved for finding the local interaction rules, and simulations are performed
to elucidate how optimal solutions can be obtained
Multi-Agent Distributed Coordination Control: Developments and Directions
In this paper, the recent developments on distributed coordination control,
especially the consensus and formation control, are summarized with the graph
theory playing a central role, in order to present a cohesive overview of the
multi-agent distributed coordination control, together with brief reviews of
some closely related issues including rendezvous/alignment, swarming/flocking
and containment control.In terms of the consensus problem, the recent results
on consensus for the agents with different dynamics from first-order,
second-order to high-order linear and nonlinear dynamics, under different
communication conditions, such as cases with/without switching communication
topology and varying time-delays, are reviewed, in which the algebraic graph
theory is very useful in the protocol designs, stability proofs and converging
analysis. In terms of the formation control problem, after reviewing the
results of the algebraic graph theory employed in the formation control, we
mainly pay attention to the developments of the rigid and persistent graphs.
With the notions of rigidity and persistence, the formation transformation,
splitting and reconstruction can be completed, and consequently the range-based
formation control laws are designed with the least required information in
order to maintain a formation rigid/persistent. Afterwards, the recent results
on rendezvous/alignment, swarming/flocking and containment control, which are
very closely related to consensus and formation control, are briefly
introduced, in order to present an integrated view of the graph theory used in
the coordination control problem. Finally, towards the practical applications,
some directions possibly deserving investigation in coordination control are
raised as well.Comment: 28 pages, 8 figure
Multi-Agent Consensus With Relative-State-Dependent Measurement Noises
In this note, the distributed consensus corrupted by relative-state-dependent
measurement noises is considered. Each agent can measure or receive its
neighbors' state information with random noises, whose intensity is a vector
function of agents' relative states. By investigating the structure of this
interaction and the tools of stochastic differential equations, we develop
several small consensus gain theorems to give sufficient conditions in terms of
the control gain, the number of agents and the noise intensity function to
ensure mean square (m. s.) and almost sure (a. s.) consensus and quantify the
convergence rate and the steady-state error. Especially, for the case with
homogeneous communication and control channels, a necessary and sufficient
condition to ensure m. s. consensus on the control gain is given and it is
shown that the control gain is independent of the specific network topology,
but only depends on the number of nodes and the noise coefficient constant. For
symmetric measurement models, the almost sure convergence rate is estimated by
the Iterated Logarithm Law of Brownian motions
Exponential Convergence of the Discrete-Time Altafini Model
This paper considers the discrete-time version of Altafini's model for
opinion dynamics in which the interaction among a group of agents is described
by a time-varying signed digraph. Prompted by an idea from [1], exponential
convergence of the system is studied using a graphical approach. Necessary and
sufficient conditions for exponential convergence with respect to each possible
type of limit states are provided. Specifically, under the assumption of
repeatedly jointly strong connectivity, it is shown that (1) a certain type of
two-clustering will be reached exponentially fast for almost all initial
conditions if, and only if, the sequence of signed digraphs is repeatedly
jointly structurally balanced corresponding to that type of two-clustering; (2)
the system will converge to zero exponentially fast for all initial conditions
if, and only if, the sequence of signed digraphs is repeatedly jointly
structurally unbalanced. An upper bound on the convergence rate is also
provided
Decentralized Event-Triggered Consensus over Unreliable Communication Networks
This article studies distributed event-triggered consensus over unreliable
communication channels. Communication is unreliable in the sense that the
broadcast channel from one agent to its neighbors can drop the event-triggered
packets of information, where the transmitting agent is unaware that the packet
was not received and the receiving agents have no knowledge of the transmitted
packet. Additionally, packets that successfully arrive at their destination may
suffer from time-varying communication delays. In this paper, we consider
directed graphs, and we also relax the consistency on the packet dropouts and
the delays. Relaxing consistency means that the delays and dropouts for a
packet broadcast by one agent can be different for each receiving node. We show
that even under this challenging scenario, agents can reach consensus
asymptotically while reducing transmissions of measurements based on the
proposed event-triggered consensus protocol. In addition, positive inter-event
times are obtained which guarantee that Zeno behavior does not occur.Comment: 20 pages, 5 figure
Guaranteed-cost consensus for multiagent networks with Lipschitz nonlinear dynamics and switching topologies
Guaranteed-cost consensus for high-order nonlinear multi-agent networks with
switching topologies is investigated. By constructing a time-varying
nonsingular matrix with a specific structure, the whole dynamics of multi-agent
networks is decomposed into the consensus and disagreement parts with nonlinear
terms, which is the key challenge to be dealt with. An explicit expression of
the consensus dynamics, which contains the nonlinear term, is given and its
initial state is determined. Furthermore, by the structure property of the
time-varying nonsingular transformation matrix and the Lipschitz condition, the
impacts of the nonlinear term on the disagreement dynamics are linearized and
the gain matrix of the consensus protocol is determined on the basis of the
Riccati equation. Moreover, an approach to minimize the guaranteed cost is
given in terms of linear matrix inequalities. Finally, the numerical simulation
is shown to demonstrate the effectiveness of theoretical results.Comment: 16 page
Dimensional-invariance principles in coupled dynamical systems-- A unified analysis and applications
In this paper we study coupled dynamical systems and investigate dimension
properties of the subspace spanned by solutions of each individual system.
Relevant problems on \textit{collinear dynamical systems} and their variations
are discussed recently by Montenbruck et. al. in \cite{collinear2017SCL}, while
in this paper we aim to provide a unified analysis to derive the
dimensional-invariance principles for networked coupled systems, and to
generalize the invariance principles for networked systems with more general
forms of coupling terms. To be specific, we consider two types of coupled
systems, one with scalar couplings and the other with matrix couplings. Via the
\textit{rank-preserving flow theory}, we show that any scalar-coupled dynamical
system (with constant, time-varying or state-dependent couplings) possesses the
dimensional-invariance principles, in that the dimension of the subspace
spanned by the individual systems' solutions remains invariant. For coupled
dynamical systems with matrix coefficients/couplings, necessary and sufficient
conditions (for constant, time-varying and state-dependent couplings) are given
to characterize dimensional-invariance principles. The proofs via a
rank-preserving matrix flow theory in this paper simplify the analysis in
\cite{collinear2017SCL}, and we also extend the invariance principles to the
cases of time-varying couplings and state-dependent couplings. Furthermore,
subspace-preserving property and signature-preserving flows are also developed
for coupled networked systems with particular coupling terms. These invariance
principles provide insightful characterizations to analyze transient behaviors
and solution evolutions for a large family of coupled systems, such as
multi-agent consensus dynamics, distributed coordination systems, formation
control systems, among others.Comment: Single column, 15 pages, 2 figures, and 2 table
- …