10,559 research outputs found
Matrix dynamics of fuzzy spheres
We study the dynamics of fuzzy two-spheres in a matrix model which represents
string theory in the presence of RR flux. We analyze the stability of known
static solutions of such a theory which contain commuting matrices and SU(2)
representations. We find that irreducible as well as reducible representations
are stable. Since the latter are of higher energy, this stability poses a
puzzle. We resolve this puzzle by noting that reducible representations have
marginal directions corresponding to non-spherical deformations. We obtain new
static solutions by turning on these marginal deformations. These solutions now
have instability or tachyonic directions. We discuss condensation of these
tachyons which correspond to classical trajectories interpolating from
multiple, small fuzzy spheres to a single, large sphere. We briefly discuss
spatially independent configurations of a D3/D5 system described by the same
matrix model which now possesses a supergravity dual.Comment: 26 pages, 3 figures, uses JHEP.cls; (v2) references adde
Scalar Solitons on the Fuzzy Sphere
We study scalar solitons on the fuzzy sphere at arbitrary radius and
noncommutativity. We prove that no solitons exist if the radius is below a
certain value. Solitons do exist for radii above a critical value which depends
on the noncommutativity parameter. We construct a family of soliton solutions
which are stable and which converge to solitons on the Moyal plane in an
appropriate limit. These solutions are rotationally symmetric about an axis and
have no allowed deformations. Solitons that describe multiple lumps on the
fuzzy sphere can also be constructed but they are not stable.Comment: 24 pages, 2 figures, typo corrected and stylistic changes. v3:
reference adde
A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems
This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version
Magnetic operations: a little fuzzy physics?
We examine the behaviour of charged particles in homogeneous, constant and/or
oscillating magnetic fields in the non-relativistic approximation. A special
role of the geometric center of the particle trajectory is elucidated. In
quantum case it becomes a 'fuzzy point' with non-commuting coordinates, an
element of non-commutative geometry which enters into the traditional control
problems. We show that its application extends beyond the usually considered
time independent magnetic fields of the quantum Hall effect. Some simple cases
of magnetic control by oscillating fields lead to the stability maps differing
from the traditional Strutt diagram.Comment: 28 pages, 8 figure
The predictive functional control and the management of constraints in GUANAY II autonomous underwater vehicle actuators
Autonomous underwater vehicle control has been a topic of research in the last decades. The challenges addressed vary depending on each research group's interests. In this paper, we focus on the predictive functional control (PFC), which is a control strategy that is easy to understand, install, tune, and optimize. PFC is being developed and applied in industrial applications, such as distillation, reactors, and furnaces. This paper presents the rst application of the PFC in autonomous underwater vehicles, as well as the simulation results of PFC, fuzzy, and gain scheduling controllers. Through simulations and navigation tests at sea, which successfully validate the performance of PFC strategy in motion control of autonomous underwater vehicles, PFC performance is compared with other control techniques such as fuzzy and gain scheduling control. The experimental tests presented here offer effective results concerning control objectives in high and intermediate levels of control. In high-level point, stabilization and path following scenarios are proven. In the intermediate levels, the results show that position and speed behaviors are improved using the PFC controller, which offers the smoothest behavior. The simulation depicting predictive functional control was the most effective regarding constraints management and control rate change in the Guanay II underwater vehicle actuator. The industry has not embraced the development of control theories for industrial systems because of the high investment in experts required to implement each technique successfully. However, this paper on the functional predictive control strategy evidences its easy implementation in several applications, making it a viable option for the industry given the short time needed to learn, implement, and operate, decreasing impact on the business and increasing immediacy.Peer ReviewedPostprint (author's final draft
Fixed points and fuzzy stability of an additive-quadratic functional equation
Ministry of Education, Science and TechnologyThe fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces have been investigated by Moslehian et al. Using fixed point method, we prove the Hyers-Ulam stability of the functional equation lf (Sigma(l)(i=1)x(i)) + Sigma(l)(i=1)f(lx(i) - Sigma(l)(i=1)d(j)) (0.1) = l(2) + l/2 Sigma(l)(i=1)f(x(i)) + l(2) - l/2 Sigma(l)(i=1)f(-x(i)) (l >= 2) in fuzzy Banach spaces.Basic Science Research Program through the National Research Foundation of Kore
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