43,254 research outputs found
Capacity of Control for Stochastic Dynamical Systems Perturbed by Mixed Fractional Brownian Motion with Delay in Control
In this paper, we discuss the relationships between capacity of control in
entropy theory and intrinsic properties in control theory for a class of finite
dimensional stochastic dynamical systems described by a linear stochastic
differential equations driven by mixed fractional Brownian motion with delay in
control. Stochastic dynamical systems can be described as an information
channel between the space of control signals and the state space. We study this
control to state information capacity of this channel in continuous time. We
turned out that, the capacity of control depends on the time of final state in
dynamical systems. By using the analysis and representation of fractional
Gaussian process, the closed form of continuous optimal control law is derived.
The reached optimal control law maximizes the mutual information between
control signals and future state over a finite time horizon. The results
obtained here are motivated by control to state information capacity for linear
systems in both types deterministic and stochastic models that are widely used
to understand information flows in wireless network information theory.
The contribution of this paper is that we propose some new relationships
between control theory and entropy theoretic properties of stochastic dynamical
systems with delay in control. Finally, we present an example that serve to
illustrate the relationships between capacity of control and intrinsic
properties in control theory.Comment: 17 pages, 2 example
Information-theoretic approach to the study of control systems
We propose an information-theoretic framework for analyzing control systems
based on the close relationship of controllers to communication channels. A
communication channel takes an input state and transforms it into an output
state. A controller, similarly, takes the initial state of a system to be
controlled and transforms it into a target state. In this sense, a controller
can be thought of as an actuation channel that acts on inputs to produce
desired outputs. In this transformation process, two different control
strategies can be adopted: (i) the controller applies an actuation dynamics
that is independent of the state of the system to be controlled (open-loop
control); or (ii) the controller enacts an actuation dynamics that is based on
some information about the state of the controlled system (closed-loop
control). Using this communication channel model of control, we provide
necessary and sufficient conditions for a system to be perfectly controllable
and perfectly observable in terms of information and entropy. In addition, we
derive a quantitative trade-off between the amount of information gathered by a
closed-loop controller and its relative performance advantage over an open-loop
controller in stabilizing a system. This work supplements earlier results [H.
Touchette, S. Lloyd, Phys. Rev. Lett. 84, 1156 (2000)] by providing new
derivations of the advantage afforded by closed-loop control and by proposing
an information-based optimality criterion for control systems. New applications
of this approach pertaining to proportional controllers, and the control of
chaotic maps are also presented.Comment: 18 pages, 7 eps figure
The Nose-hoover thermostated Lorentz gas
We apply the Nose-Hoover thermostat and three variations of it, which control
different combinations of velocity moments, to the periodic Lorentz gas.
Switching on an external electric field leads to nonequilibrium steady states
for the four models with a constant average kinetic energy of the moving
particle. We study the probability density, the conductivity and the attractor
in nonequilibrium and compare the results to the Gaussian thermostated Lorentz
gas and to the Lorentz gas as thermostated by deterministic scattering.Comment: 7 pages (revtex) with 10 figures (postscript), most of the figures
are bitmapped with low-resolution. The originals are many MB, they can be
obtained upon reques
A posteriori error analysis and adaptive non-intrusive numerical schemes for systems of random conservation laws
In this article we consider one-dimensional random systems of hyperbolic
conservation laws. We first establish existence and uniqueness of random
entropy admissible solutions for initial value problems of conservation laws
which involve random initial data and random flux functions. Based on these
results we present an a posteriori error analysis for a numerical approximation
of the random entropy admissible solution. For the stochastic discretization,
we consider a non-intrusive approach, the Stochastic Collocation method. The
spatio-temporal discretization relies on the Runge--Kutta Discontinuous
Galerkin method. We derive the a posteriori estimator using continuous
reconstructions of the discrete solution. Combined with the relative entropy
stability framework this yields computable error bounds for the entire
space-stochastic discretization error. The estimator admits a splitting into a
stochastic and a deterministic (space-time) part, allowing for a novel
residual-based space-stochastic adaptive mesh refinement algorithm. We conclude
with various numerical examples investigating the scaling properties of the
residuals and illustrating the efficiency of the proposed adaptive algorithm
From Knowledge, Knowability and the Search for Objective Randomness to a New Vision of Complexity
Herein we consider various concepts of entropy as measures of the complexity
of phenomena and in so doing encounter a fundamental problem in physics that
affects how we understand the nature of reality. In essence the difficulty has
to do with our understanding of randomness, irreversibility and
unpredictability using physical theory, and these in turn undermine our
certainty regarding what we can and what we cannot know about complex phenomena
in general. The sources of complexity examined herein appear to be channels for
the amplification of naturally occurring randomness in the physical world. Our
analysis suggests that when the conditions for the renormalization group apply,
this spontaneous randomness, which is not a reflection of our limited
knowledge, but a genuine property of nature, does not realize the conventional
thermodynamic state, and a new condition, intermediate between the dynamic and
the thermodynamic state, emerges. We argue that with this vision of complexity,
life, which with ordinary statistical mechanics seems to be foreign to physics,
becomes a natural consequence of dynamical processes.Comment: Phylosophica
- …