3,851 research outputs found
Event-Triggered Algorithms for Leader-Follower Consensus of Networked Euler-Lagrange Agents
This paper proposes three different distributed event-triggered control
algorithms to achieve leader-follower consensus for a network of Euler-Lagrange
agents. We firstly propose two model-independent algorithms for a subclass of
Euler-Lagrange agents without the vector of gravitational potential forces. By
model-independent, we mean that each agent can execute its algorithm with no
knowledge of the agent self-dynamics. A variable-gain algorithm is employed
when the sensing graph is undirected; algorithm parameters are selected in a
fully distributed manner with much greater flexibility compared to all previous
work concerning event-triggered consensus problems. When the sensing graph is
directed, a constant-gain algorithm is employed. The control gains must be
centrally designed to exceed several lower bounding inequalities which require
limited knowledge of bounds on the matrices describing the agent dynamics,
bounds on network topology information and bounds on the initial conditions.
When the Euler-Lagrange agents have dynamics which include the vector of
gravitational potential forces, an adaptive algorithm is proposed which
requires more information about the agent dynamics but can estimate uncertain
agent parameters.
For each algorithm, a trigger function is proposed to govern the event update
times. At each event, the controller is updated, which ensures that the control
input is piecewise constant and saves energy resources. We analyse each
controllers and trigger function and exclude Zeno behaviour. Extensive
simulations show 1) the advantages of our proposed trigger function as compared
to those in existing literature, and 2) the effectiveness of our proposed
controllers.Comment: Extended manuscript of journal submission, containing omitted proofs
and simulation
Dynamic Multilevel Graph Visualization
We adapt multilevel, force-directed graph layout techniques to visualizing
dynamic graphs in which vertices and edges are added and removed in an online
fashion (i.e., unpredictably). We maintain multiple levels of coarseness using
a dynamic, randomized coarsening algorithm. To ensure the vertices follow
smooth trajectories, we employ dynamics simulation techniques, treating the
vertices as point particles. We simulate fine and coarse levels of the graph
simultaneously, coupling the dynamics of adjacent levels. Projection from
coarser to finer levels is adaptive, with the projection determined by an
affine transformation that evolves alongside the graph layouts. The result is a
dynamic graph visualizer that quickly and smoothly adapts to changes in a
graph.Comment: 21 page
Burgers Turbulence
The last decades witnessed a renewal of interest in the Burgers equation.
Much activities focused on extensions of the original one-dimensional
pressureless model introduced in the thirties by the Dutch scientist J.M.
Burgers, and more precisely on the problem of Burgers turbulence, that is the
study of the solutions to the one- or multi-dimensional Burgers equation with
random initial conditions or random forcing. Such work was frequently motivated
by new emerging applications of Burgers model to statistical physics,
cosmology, and fluid dynamics. Also Burgers turbulence appeared as one of the
simplest instances of a nonlinear system out of equilibrium. The study of
random Lagrangian systems, of stochastic partial differential equations and
their invariant measures, the theory of dynamical systems, the applications of
field theory to the understanding of dissipative anomalies and of multiscaling
in hydrodynamic turbulence have benefited significantly from progress in
Burgers turbulence. The aim of this review is to give a unified view of
selected work stemming from these rather diverse disciplines.Comment: Review Article, 49 pages, 43 figure
Event-Triggered Consensus and Formation Control in Multi-Agent Coordination
The focus of this thesis is to study distributed event-triggered
control for multi-agent systems (MASs) facing constraints in
practical applications. We consider several problems in the
field, ranging from event-triggered consensus with information
quantization, event-triggered edge agreement under
synchronized/unsynchronized clocks, event-triggered
leader-follower consensus with Euler-Lagrange agent dynamics and
cooperative event-triggered rigid formation control.
The first topic is named as event-triggered consensus with
quantized relative state measurements. In this topic, we develop
two event-triggered controllers with quantized relative state
measurements to achieve consensus for an undirected network where
each agent is modelled by single integrator dynamics. Both
uniform and logarithmic quantizers are considered, which,
together with two different controllers, yield four cases of
study in this topic. The quantized information is used to update
the control input as well as to determine the next trigger event.
We show that approximate consensus can be achieved by the
proposed algorithms and Zeno behaviour can be completely excluded
if constant offsets with some computable lower bounds are added
to the trigger conditions.
The second topic considers event-triggered edge agreement
problems. Two cases, namely the synchronized clock case and the
unsynchronized clock case, are studied. In the synchronized clock
case, all agents are activated simultaneously to measure the
relative state information over edge links under a global clock.
Edge events are defined and their occurrences trigger the update
of control inputs for the two agents sharing the link. We show
that average consensus can be achieved with our proposed
algorithm. In the unsynchronized clock case, each agent executes
control algorithms under its own clock which is not synchronized
with other agents' clocks. An edge event only triggers control
input update for an individual agent. It is shown that all agents
will reach consensus in a totally asynchronous manner.
In the third topic, we propose three different distributed
event-triggered control algorithms to achieve leader-follower
consensus for a network of Euler-Lagrange agents. We firstly
propose two model-independent algorithms for a subclass of
Euler-Lagrange agents without the vector of gravitational
potential forces. A variable-gain algorithm is employed when the
sensing graph is undirected; algorithm parameters are selected in
a fully distributed manner with much greater flexibility compared
to all previous work concerning event-triggered consensus
problems. When the sensing graph is directed, a constant-gain
algorithm is employed. The control gains must be centrally
designed to exceed several lower bounding inequalities which
require limited knowledge of bounds on the matrices describing
the agent dynamics, bounds on network topology information and
bounds on the initial conditions. When the Euler-Lagrange agents
have dynamics which include the vector of gravitational potential
forces, an adaptive algorithm is proposed. This requires more
information about the agent dynamics but allows for the
estimation of uncertain agent parameters.
The last topic discusses cooperative stabilization control of
rigid formations via an event-triggered approach. We first design
a centralized event-triggered formation control system, in which
a central event controller determines the next triggering time
and broadcasts the event signal to all the agents for control
input update. We then build on this approach to propose a
distributed event control strategy, in which each agent can use
its local event trigger and local information to update the
control input at its own event time. For both cases, the trigger
condition, event function and trigger behaviour are discussed in
detail, and the exponential convergence of the formation system
is guaranteed
Attitude Synchronization of Spacecraft Formation with Optimization and Adaptation of Consensus Penalty Terms
The contribution of this thesis is on the temporal adjustment of the consensus weights, as applied to spacecraft formation control. Such an objective is attained by dynamically enforcing attitude synchronization via coupling terms included in each spacecraft controller. It is assumed that each spacecraft has identical dynamics but with unknown inertia parameters and external disturbances. By augmenting a standard adaptive controller that accounts for the unknown parameters, made feasible via an assumption on parameterization, with adaptation of the consensus weights, one opts to improve spacecraft synchronization. The coupling terms, responsible for enforcing synchronization amongst spacecraft, are weighted dynamically in proportion to the disagreement between the states of the spacecraft. The time adjustment of edge-dependent gains as well as the special cases of node-dependent and agent-independent constant gains are derived using Lyapunov redesign methods. The proposed adaptive control architectures which allow for adaptation of both parameter uncertainties and consensus penalty terms are demonstrated via extensive numerical studies of spacecraft networks with limited connectivity. By considering the sum of deviation-from-the-mean and rotational kinetic energy as appropriate metrics for synchronization and controller performance, the numerical studies also provide insights on the choice of optimal consensus gains
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