2,071 research outputs found
Bounds for Invariance Pressure
This paper provides an upper for the invariance pressure of control sets with
nonempty interior and a lower bound for sets with finite volume. In the special
case of the control set of a hyperbolic linear control system in R^{d} this
yields an explicit formula. Further applications to linear control systems on
Lie groups and to inner control sets are discussed.Comment: 16 page
Invariance Entropy of Hyperbolic Control Sets
In this paper, we improve the known estimates for the invariance entropy of a
nonlinear control system. For sets of complete approximate controllability we
derive an upper bound in terms of Lyapunov exponents and for uniformly
hyperbolic sets we obtain a similar lower bound. Both estimates can be applied
to hyperbolic chain control sets, and we prove that under mild assumptions they
can be merged into a formula
Explicit approximate controllability of the Schr\"odinger equation with a polarizability term
We consider a controlled Schr\"odinger equation with a dipolar and a
polarizability term, used when the dipolar approximation is not valid. The
control is the amplitude of the external electric field, it acts non linearly
on the state. We extend in this infinite dimensional framework previous
techniques used by Coron, Grigoriu, Lefter and Turinici for stabilization in
finite dimension. We consider a highly oscillating control and prove the
semi-global weak stabilization of the averaged system using a Lyapunov
function introduced by Nersesyan. Then it is proved that the solutions of the
Schr\"odinger equation and of the averaged equation stay close on every finite
time horizon provided that the control is oscillating enough. Combining these
two results, we get approximate controllability to the ground state for the
polarizability system
Systems control theory applied to natural and synthetic musical sounds
Systems control theory is a far developped field which helps to study stability, estimation and control of dynamical systems. The physical behaviour of musical instruments, once described by dynamical systems, can then be controlled and numerically simulated for many purposes.
The aim of this paper is twofold: first, to provide the theoretical background on linear system theory, both in continuous and discrete time, mainly in the case of a finite number of degrees of freedom ; second, to give illustrative examples on wind instruments, such as the vocal tract represented as a waveguide, and a sliding flute
Asymptotic ensemble stabilizability of the Bloch equation
In this paper we are concerned with the stabilizability to an equilibrium
point of an ensemble of non interacting half-spins. We assume that the spins
are immersed in a static magnetic field, with dispersion in the Larmor
frequency, and are controlled by a time varying transverse field. Our goal is
to steer the whole ensemble to the uniform "down" position. Two cases are
addressed: for a finite ensemble of spins, we provide a control function (in
feedback form) that asymptotically stabilizes the ensemble in the "down"
position, generically with respect to the initial condition. For an ensemble
containing a countable number of spins, we construct a sequence of control
functions such that the sequence of the corresponding solutions pointwise
converges, asymptotically in time, to the target state, generically with
respect to the initial conditions. The control functions proposed are uniformly
bounded and continuous
Geometric control of particle manipulation in a two-dimensional fluid
Manipulation of particles suspended in fluids is crucial for many applications, such as precision machining, chemical processes, bio-engineering, and self-feeding of microorganisms. In this paper, we study the problem of particle manipulation by cyclic fluid boundary excitations from a geometric-control viewpoint. We focus on the simplified problem of manipulating a single particle by generating controlled cyclic motion of a circular rigid body in a two-dimensional perfect fluid. We show that the drift in the particle location after one cyclic motion of the body can be interpreted as the geometric phase of a connection induced by the system's hydrodynamics. We then formulate the problem as a control system, and derive a geometric criterion for its nonlinear controllability. Moreover, by exploiting the geometric structure of the system, we explicitly construct a feedback-based gait that results in attraction of the particle towards the rigid body. We argue that our gait is robust and model-independent, and demonstrate it in both perfect fluid and Stokes fluid
Delocalization of quasimodes on the disk
This note deals with semiclassical measures associated to {(sufficiently
accurate)} quasimodes for the Laplace-Dirichlet operator on the disk.
In this time-independent set-up, we simplify the statements of our preprint
arXiv:1406.0681 and their proofs. We describe the restriction of semiclassical
measures to every invariant torus in terms of two-microlocal measures. As
corollaries, we show regularity and delocalization properties for limit
measures of : these are absolutely continuous in the interior of
the disk and charge every open set intersecting the boundary.Comment: arXiv admin note: text overlap with arXiv:1406.068
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