5,624 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
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
Quasilinear approach of the cumulative whistler instability in fast solar winds: Constraints of electron temperature anisotropy
Context. Solar outflows are a considerable source of free energy which
accumulates in multiple forms like beaming (or drifting) components and/or
temperature anisotropies. However, kinetic anisotropies of plasma particles do
not grow indefinitely and particle-particle collisions are not efficient enough
to explain the observed limits of these anisotropies. Instead, the
self-generated wave instabilities can efficiently act to constrain kinetic
anisotropies, but the existing approaches are simplified and do not provide
satisfactory explanations. Thus, small deviations from isotropy shown by the
electron temperature () in fast solar winds are not explained yet.
Aims. This paper provides an advanced quasilinear description of the whistler
instability driven by the anisotropic electrons in conditions typical for the
fast solar winds. The enhanced whistler-like fluctuations may constrain the
upper limits of temperature anisotropy ,
where are defined with respect to the magnetic field
direction.
Methods. Studied are the self-generated whistler instabilities, cumulatively
driven by the temperature anisotropy and the relative (counter)drift of the
electron populations, e.g., core and halo electrons. Recent studies have shown
that quasi-stable states are not bounded by the linear instability thresholds
but an extended quasilinear approach is necessary to describe them in this
case.
Results. Marginal conditions of stability are obtained from a quasilinear
theory of the cumulative whistler instability, and approach the quasi-stable
states of electron populations reported by the observations.The instability
saturation is determined by the relaxation of both the temperature anisotropy
and the relative drift of electron populations.Comment: Accepted for publication in A&
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