Property:Abstract
From Murray Wiki
Jump to navigationJump to search
This is a property of type Text.
O
In this paper we investigate the optimal control of affine connection
control systems. The formalism of the affine connection can be used to
describe geometrically the dynamics of me chanical systems, including those
with nonholonomic constraints. In the standard variational approach to such
problems, one converts an n dimensional second order system into a 2n
dimensional first order system, and uses these equations as constraints on
the optimization. An alternative approach, which we develop in this paper,
is to include the system dynamics as second order constraints of the
optimization, and optimize relative to variations in the configuration
space. Using the affine connection, its associated tensors, and the notion
of covariant differentiation, we show how variations in the configuration
space induce variations in the tangent space. In this setting, we derive
second order equations have a geometric formulation parallel to that of the
system dynamics. They also specialize to results found in the literature. +
In this paper we look at the problem of multi-sensor data fusion when data is being communicated over
channels that drop packets randomly. We are motivated by
the use of wireless links for communication among nodes in
upcoming sensor networks. We wish to identify the information that should be communicated by each node to others given
that some of the information it had transmitted earlier might
have been lost. We solve the problem exactly for the case
of two sensors and study the performance of the algorithm
when more sensors are present. For the two-sensor case, the
performance of our algorithm is optimal in the sense that if
a packet is received from the other sensor, it is equivalent to
receiving all previous measurements, irrespective of the packet
drop pattern. +
N
In this paper we present a control law for globally asymptotically stabilizing a class
of controllable nonlinear systems without drift. The control law converts into closed loop
feedback earlier strategies for open loop steering of nonholonomic systems using sinusoids
at integrally related frequencies. The global result is obtained by introducing saturation
functions. Simulation results for stabilizing a simple kinematic model of an automobile
are included. +
C
In this paper we present a definition of "configuration controllability" for
mechanical systems whose Lagrangian is kinetic energy with respect to a Riemannian metric
minus potential energy. A computable test for this new version of controllability is also
derived. This condition involves a new object which we call the symmetric product. Of
particular interest is a definition of "equilibrium controllability" for which
we are able to derive computable sufficient conditions. Examples illustrate the theory. +
In this paper we present a dynamical systems framework for analyzing multi-agent rendezvous problems
and characterize the dynamical behavior of the collective system. Recently, the problem of rendezvous has been
addressed considerably in the graph theoretic framework, which is strongly based on the communication aspects of
the problem. The proposed approach is based on set invariance theory and focusses on how to generate feedback
between the vehicles, a key part of the rendezvous problem. The rendezvous problem is defined on the positions
of the agents and the dynamics is modeled as linear first order systems. The proposed framework however is not
fundamentally limited to linear first order dynamics and can be extended to analyze rendezvous of higher order agents. +
A
In this paper we present a dynamical systems representation for multi-agent rendezvous on
the phase plane. We restrict our attention to two agents, each with scalar dynamics. The problem of rendezvous is cast as a stabilization problem, with a set of constraints on the trajectories
of the agents, defined on the phase plane. We also describe a method to generate control Lyapunov functions that when used in conjunction with a stabilizing control law, such as Sontag's
formula, make sure that the two-agent system attains rendezvous. The main result of this paper
is a Lyapunov-like certificate theorem that describes a set of constraints, which when satisfied
are su±cient to guarantee rendezvous. +
V
In this paper we present two methods, the nonholonomic method and the vakonomic
method, for deriving equations of motion for a mechanical system with constraints. The
resulting equations are compared. Results are also presented from an experiment for a
model system: a ball rolling without sliding on a rotating table. Both sets of equations
of motion for the model system are compared with the experimental results. The effects of
various forms of friction are considered in the nonholonomic equations. With appropriate
friction terms, the nonholonomic equations of motion for the model system give reasonable
agreement with the experimental observations. +
N
In this paper we provide new design principles
for estimation over wireless fading channels in mobile sensor
networks. We show how to optimize receiver and transmitter
designs to improve estimation performance in the application
layer. On the receiver side, we show that the optimum packet
drop mechanism is the one that provides a balance between
information loss and communication noise. On the transmitter
side, we show how to optimize and adapt the transmission
rate for performance improvement in the application layer.
We further provide stability conditions for different design
strategies. The work confirms that delay-sensitive mobile
sensor applications require new design paradigms and applying
the same design principles of data networks can lead
to performance degradation. The work also highlights the
importance of cross-layer feedback and provides alternative
designs if such feedbacks are not available. +
S
In this paper we study the problem of synthesizing correct-by-construction Behavior Trees (BTs) controlling agents in adversarial environments. The proposed approach combines the modularity and reactivity of BTs with the formal guarantees of Linear Temporal Logic (LTL) methods. Given a set of admissible environment specifications, an agent model in form of a Finite Transition System and the desired task in form of an LTL formula, we synthesize a BT in polynomial time, that is guaranteed to correctly execute the desired task. To illustrate the approach, we present three examples of increasing complexity. +
P
In this paper we study the stabilization problem for control systems
defined on SE(3), the Euclidean group of rigid--body motions.
Assuming one actuator is available for each degree of freedom, we
exploit geometric properties of Lie groups (and corresponding Lie
algebras) to generalize the classical PD control in a coordinate--free
way. For the SO(3) case, the compactness of the group gives rise to a
natural metric structure and to a natural choice of preferred control
direction: an optimal (in the sense of geodesic) solution is given to
the attitude control problem. In the SE(3) case, no natural metric is
uniquely defined, so that more freedom is left in the control design.
Different formulations of PD feedback can be adopted by extending the
SO(3) approach to the whole of SE(3) or by breaking the problem into a
control problem on SO(3) x R^3. For the simple SE(2) case,
simulations are reported to illustrate the behavior of the different
choices. Finally, we discuss the trajectory tracking problem and show
how to reduce it to a stabilization problem, mimicking the usual
approach in R^n. +
E
In this paper we use ellipsoidal cones to achieve
rendezvous of multiple agents. Rendezvous of multiple
agents is shown to be equivalent to ellipsoidal cone invariance
and a controller synthesis framework is presented.
We first demonstrate the methodology on first order LTI
systems and then extend it to rendezvous of mechanical
systems, that is systems that are force driven. +
In this paper, a cascade discrete-continuous state estimator on a partial
order is proposed and its existence investigated. The continuous state estimation
error is bounded by a monotonically nonincreasing function of the discrete state
estimation error, with both the estimation errors converging to zero. This work
shows that the lattice approach to estimation is general as the proposed estimator
can be constructed for any observable and discrete state observable system.
The main advantage of using the lattice approach for estimation becomes clear
when the system has monotone properties that can be exploited in the estimator
design. In such a case, the computational complexity of the estimator can be drastically
reduced and tractability can be achieved. Some examples are proposed to
illustrate these ideas. +
In this paper, we analyze the oscillatory dynamics of a class of cyclic gene regulatory networks and provide engineering principles for the robust synthesis of biochemical oscillators. We first review the first authorâs previous result that the oscillatory parameter regime of the gene regulatory circuits can be rigorously explored by the local stability analysis of a unique equilibrium. The local stability analysis then leads to the first engineering principle that the circuit components, or genes, should be chosen so that the kinetic profiles of the circuit components are similar to each other. Using a homogeneous oscillator model, we further discuss how to reduce the cell-to-cell variability of the oscillators that is caused by intrinsic noise. +
A
In this paper, we analyze the problem of bifurcation control from a
geometric perspective. Our goal is to provide coordinate free,
geometric conditions under which control can be used to alter the
bifurcation properties of a nonlinear control system. These
insights are expected to be useful in understanding the role that
magnitude and rate limits play in bifurcation control, as well as
giving deeper understanding of the types of control inputs that are
required to alter the nonlinear dynamics of bifurcating systems. We
also use a model from active control of rotating stall in axial
compression systems to illustrate the geometric sufficient
conditions of stabilizability. +
In this paper, we approximate models of interconnected
systems that are to be used for decentralized control
design. The suggested approach is based on approximation of
so-called subnetwork models. A subnetwork model is a model
of the interconnected system, as seen from one specific
position
in the network. The simplification is done by using
weighted model reduction, and several approximation
criteria
are given. A new method for weighted model reduction is
used.
The method is based on a combination of known techniques
that use semidefinite programming and frequency-data
samples
of transfer functions. The method is guaranteed to preserve
stability and does not depend strongly on the order of the
original model. This is particularly important for large
interconnected systems. Two examples are given to
illustrate the technique. +
K
In this paper, we consider Kalman filtering over a packet-delaying network. Given the probability distribution of the delay, we
can completely characterize the filter performance via a probabilistic approach. We assume the estimator maintains a buffer of length D so that at each time k, the estimator is able to retrieve all available data packets up to time k â D + 1. Both the cases of sensor with and without necessary computation capability for filter updates are considered. When the sensor has no computation capability, for a given D, we give lower and upper bounds on the probability for which the estimation error covariance is within a prescribed bound. When the sensor has computation capability, we show that the previously derived lower and upper bounds are equal to each other. An approach for determining the minimum buffer length for a required performance in probability is given and an evaluation on the number of expected filter updates is provided. Examples are provided to demonstrate the theory developed in the paper. +
E
In this paper, we consider a discrete time state
estimation problem over a packet-based network. In each
discrete time step, the measurement is sent to a Kalman
filter with some probability that it is received or dropped.
Previous pioneering work on Kalman filtering with intermittent
observation losses shows that there exists a certain threshold of
the packet dropping rate below which the estimator is stable in
the expected sense. In their analysis, they assume that packets
are dropped independently between all time steps. However we
give a completely different point of view. On the one hand, it
is not required that the packets are dropped independently but
just that the information gain pi_g, defined to be the limit of the
ratio of the number of received packets n during N time steps
as N goes to infinity, exists. On the other hand, we show that
for any given pi_g, as long as pi_g > 0, the estimator is stable
almost surely, i.e. for any given epsilon > 0 the error covariance
matrix P{k is bounded by a finite matrix M, with probability
1 â epsilon. Given an error tolerance M, pi_g can in turn be found.
We also give explicit formula for the relationship between M
and epsilon. +
R
In this paper, we consider a robust network
control problem. We consider linear unstable and uncertain
discrete time plants with a network between the sensors and
controller and the controller and plant. We investigate two
defining characteristics of network controlled systems and the
impact of uncertainty on these. Namely, the minimum data rates
required for the two networks and the tolerable data drop out
in the form of packet losses. We are able to derive sufficient
conditions in terms of the minimum data rate and minimum
packet arrival rate to ensure stability of the closed loop system. +
T
In this paper, we consider a robust network
control problem. We consider linear unstable and uncertain
discrete time plants with a network between the sensor and
controller and the controller and plant. We investigate the
effect of data drop out in the form of packet losses. Four
distinct control schemes are explored and sufficient conditions
to ensure almost sure stability of the closed loop system are
derived for each of them in terms of minimum packet arrival
rate and the maximum uncertainty. +
C
In this paper, we consider a robust networked control problem. We consider linear unstable and uncertain discrete time plants with a network between the sensor and controller as well as between
the controller and plant. We investigate the effect of data drop out in the form of packet losses and
we focus on the tradeoff between packet arrival rate versus the uncertainties of the system dynamics. We show that the minimum packet arrival rate and the maximum uncertainty of the system dynamics have a positive correlation. Four distinct control schemes are
explored and serve as examples to study this tradeoff. We derive sufficient condition for each scheme to ensure almost sure stability of the closed loop system. Simulation and examples are provided to assist the theory. +
