441 research outputs found
Algebraic methods for dynamic systems
Algebraic methods for application to dynamic control system
Lag synchronization and scaling of chaotic attractor in coupled system
We report a design of delay coupling for lag synchronization in two
unidirectionally coupled chaotic oscillators. A delay term is introduced in the
definition of the coupling to target any desired lag between the driver and the
response. The stability of the lag synchronization is ensured by using the
Hurwitz matrix stability. We are able to scale up or down the size of a driver
attractor at a response system in presence of a lag. This allows compensating
the attenuation of the amplitude of a signal during transmission through a
delay line. The delay coupling is illustrated with numerical examples of 3D
systems, the Hindmarsh-Rose neuron model, the R\"ossler system and a Sprott
system and, a 4D system. We implemented the coupling in electronic circuit to
realize any desired lag synchronization in chaotic oscillators and scaling of
attractors.Comment: 10 pages, 7 figure
A Scalable, Self-Analyzing Digital Locking System for use on Quantum Optics Experiments
Digital control of optics experiments has many advantages over analog control
systems, specifically in terms of scalability, cost, flexibility, and the
integration of system information into one location. We present a digital
control system, freely available for download online, specifically designed for
quantum optics experiments that allows for automatic and sequential re-locking
of optical components. We show how the inbuilt locking analysis tools,
including a white-noise network analyzer, can be used to help optimize
individual locks, and verify the long term stability of the digital system.
Finally, we present an example of the benefits of digital locking for quantum
optics by applying the code to a specific experiment used to characterize
optical Schrodinger cat states.Comment: 7 pages, 5 figure
Analysis and design of solid-state circuits utilizing the NASA analysis computer program Annual report
Network Analysis for Systems Application Program /NASAP/ applicable in analysis and design of solid state circuit
Testimony to the Senate Judiciary Committee by the ERA Project at Columbia Law School and Constitutional Law Scholars on Joint Resolution S.J.Res. 4: Removing the Deadline for the Ratification of the Equal Rights Amendment
The Equal Rights Amendment Project at Columbia Law School (ERA Project) and the undersigned constitutional law scholars provide the following analysis of S.J.Res. 4, resolving to remove the time limit for the ratification of the Equal Rights Amendment (ERA) and declaring the ERA fully ratified
Information capacity in the weak-signal approximation
We derive an approximate expression for mutual information in a broad class
of discrete-time stationary channels with continuous input, under the
constraint of vanishing input amplitude or power. The approximation describes
the input by its covariance matrix, while the channel properties are described
by the Fisher information matrix. This separation of input and channel
properties allows us to analyze the optimality conditions in a convenient way.
We show that input correlations in memoryless channels do not affect channel
capacity since their effect decreases fast with vanishing input amplitude or
power. On the other hand, for channels with memory, properly matching the input
covariances to the dependence structure of the noise may lead to almost
noiseless information transfer, even for intermediate values of the noise
correlations. Since many model systems described in mathematical neuroscience
and biophysics operate in the high noise regime and weak-signal conditions, we
believe, that the described results are of potential interest also to
researchers in these areas.Comment: 11 pages, 4 figures; accepted for publication in Physical Review
Continuous quantum feedback of coherent oscillations in a solid-state qubit
We have analyzed theoretically the operation of the Bayesian quantum feedback
of a solid-state qubit, designed to maintain perfect coherent oscillations in
the qubit for arbitrarily long time. In particular, we have studied the
feedback efficiency in presence of dephasing environment and detector
nonideality. Also, we have analyzed the effect of qubit parameter deviations
and studied the quantum feedback control of an energy-asymmetric qubit.Comment: 11 page
Design of coupling for synchronization in time-delayed systems
We report a design of delay coupling for targeting desired synchronization in
delay dynamical systems. We target synchronization, antisynchronization, lag-,
antilag- synchronization, amplitude death (or oscillation death) and
generalized synchronization in mismatched oscillators. A scaling of the size of
an attractor is made possible in different synchronization regimes. We realize
a type of mixed synchronization where synchronization, antisynchronization
coexist in different pairs of state variables of the coupled system. We
establish the stability condition of synchronization using the
Krasovskii-Lyapunov function theory and the Hurwitz matrix criterion. We
present numerical examples using the Mackey-Glass system and a delay
R\"{o}ssler system.Comment: 8 pages, 6 figures; Chaos 22 (2012
Synthesis of multi-loop automatic control systems by the nonlinear programming method
The article deals with the problem of calculation of the multi-loop control systems optimal tuning parameters by numerical methods and nonlinear programming methods. For this purpose, in the paper the Optimization Toolbox of Matlab is used
Formalising the Continuous/Discrete Modeling Step
Formally capturing the transition from a continuous model to a discrete model
is investigated using model based refinement techniques. A very simple model
for stopping (eg. of a train) is developed in both the continuous and discrete
domains. The difference between the two is quantified using generic results
from ODE theory, and these estimates can be compared with the exact solutions.
Such results do not fit well into a conventional model based refinement
framework; however they can be accommodated into a model based retrenchment.
The retrenchment is described, and the way it can interface to refinement
development on both the continuous and discrete sides is outlined. The approach
is compared to what can be achieved using hybrid systems techniques.Comment: In Proceedings Refine 2011, arXiv:1106.348
- …