7,065 research outputs found
Flexible Lyapunov Functions and Applications to Fast Mechatronic Systems
The property that every control system should posses is stability, which
translates into safety in real-life applications. A central tool in systems
theory for synthesizing control laws that achieve stability are control
Lyapunov functions (CLFs). Classically, a CLF enforces that the resulting
closed-loop state trajectory is contained within a cone with a fixed,
predefined shape, and which is centered at and converges to a desired
converging point. However, such a requirement often proves to be
overconservative, which is why most of the real-time controllers do not have a
stability guarantee. Recently, a novel idea that improves the design of CLFs in
terms of flexibility was proposed. The focus of this new approach is on the
design of optimization problems that allow certain parameters that define a
cone associated with a standard CLF to be decision variables. In this way
non-monotonicity of the CLF is explicitly linked with a decision variable that
can be optimized on-line. Conservativeness is significantly reduced compared to
classical CLFs, which makes \emph{flexible CLFs} more suitable for
stabilization of constrained discrete-time nonlinear systems and real-time
control. The purpose of this overview is to highlight the potential of flexible
CLFs for real-time control of fast mechatronic systems, with sampling periods
below one millisecond, which are widely employed in aerospace and automotive
applications.Comment: 2 figure
Towards parallelizable sampling-based Nonlinear Model Predictive Control
This paper proposes a new sampling-based nonlinear model predictive control
(MPC) algorithm, with a bound on complexity quadratic in the prediction horizon
N and linear in the number of samples. The idea of the proposed algorithm is to
use the sequence of predicted inputs from the previous time step as a warm
start, and to iteratively update this sequence by changing its elements one by
one, starting from the last predicted input and ending with the first predicted
input. This strategy, which resembles the dynamic programming principle, allows
for parallelization up to a certain level and yields a suboptimal nonlinear MPC
algorithm with guaranteed recursive feasibility, stability and improved cost
function at every iteration, which is suitable for real-time implementation.
The complexity of the algorithm per each time step in the prediction horizon
depends only on the horizon, the number of samples and parallel threads, and it
is independent of the measured system state. Comparisons with the fmincon
nonlinear optimization solver on benchmark examples indicate that as the
simulation time progresses, the proposed algorithm converges rapidly to the
"optimal" solution, even when using a small number of samples.Comment: 9 pages, 9 pictures, submitted to IFAC World Congress 201
Is the Weibel instability enhanced by the suprathermal populations, or not?
The kinetic instabilities of the Weibel-type are presently invoked in a large
variety of astrophysical scenarios because anisotropic plasma structures are
ubiquitous in space. The Weibel instability is driven by a temperature
anisotropy which is commonly modeled by a bi-axis distribution function, such
as a bi-Maxwellian or a generalized bi-Kappa. Previous studies have been
limited to a bi-Kappa distribution and found a suppression of this instability
in the presence of suprathermal tails. In the present paper it is shown that
the Weibel growth rate is rather more sensitive to the shape of the anisotropic
distribution function. In order to illustrate the distinguishing properties of
this instability a \emph{product-bi-Kappa distribution} is introduced, with the
advantage that this distribution function enables the use of different values
of the spectral index in the two directions, . The growth rates and the instability threshold are derived and
contrasted with those for a simple bi-Kappa and a bi-Maxwellian. Thus, while
the maximum growth rates reached at the saturation are found to be higher, the
threshold is drastically reduced making the anisotropic product-bi-Kappa (with
small kappas) highly susceptible to the Weibel instability. This effect could
also rise questions on the temperature or the temperature anisotropy that seems
to be not an exclusive source of free energy for this instability, and
definition of these notions for such Kappa distributions must probably be
reconsidered
Cartan's spiral staircase in physics and, in particular, in the gauge theory of dislocations
In 1922, Cartan introduced in differential geometry, besides the Riemannian
curvature, the new concept of torsion. He visualized a homogeneous and
isotropic distribution of torsion in three dimensions (3d) by the "helical
staircase", which he constructed by starting from a 3d Euclidean space and by
defining a new connection via helical motions. We describe this geometric
procedure in detail and define the corresponding connection and the torsion.
The interdisciplinary nature of this subject is already evident from Cartan's
discussion, since he argued - but never proved - that the helical staircase
should correspond to a continuum with constant pressure and constant internal
torque. We discuss where in physics the helical staircase is realized: (i) In
the continuum mechanics of Cosserat media, (ii) in (fairly speculative) 3d
theories of gravity, namely a) in 3d Einstein-Cartan gravity - this is Cartan's
case of constant pressure and constant intrinsic torque - and b) in 3d Poincare
gauge theory with the Mielke-Baekler Lagrangian, and, eventually, (iii) in the
gauge field theory of dislocations of Lazar et al., as we prove for the first
time by arranging a suitable distribution of screw dislocations. Our main
emphasis is on the discussion of dislocation field theory.Comment: 31 pages, 8 figure
Effects of suprathermal electrons on the proton temperature anisotropy in space plasmas: Electromagnetic ion-cyclotron instability
In collision-poor plasmas from space, e.g., the solar wind and planetary
magnetospheres, the kinetic anisotropy of the plasma particles is expected to
be regulated by the kinetic instabilities. Driven by an excess of ion (proton)
temperature perpendicular to the magnetic field , the
electromagnetic ion-cyclotron (EMIC) instability is fast enough to constrain
the proton anisotropy, but the observations do not conform to the instability
thresholds predicted by the standard theory for bi-Maxwellian models of the
plasma particles. This paper presents an extended investigation of the EMIC
instability in the presence of suprathermal electrons which are ubiquitous in
these environments. The analysis is based on the kinetic (Vlasov-Maxwell)
theory assuming that both species, protons and electrons, may be anisotropic,
and the EMIC unstable solutions are derived numerically providing an accurate
description for conditions typically encountered in space plasmas. The effects
of suprathermal populations are triggered by the electron anisotropy and the
temperature contrast between electrons and protons. For certain conditions the
anisotropy thresholds exceed the limits of the proton anisotropy measured in
the solar wind considerably restraining the unstable regimes of the EMIC modes.Comment: Accepted for publication in Astrophysics and space scienc
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