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576
We study a model describing vibrations of a cylindrical domain with thickness e > 0. A characteristic of this model is that it contains pollution terms in the boundary data and missing terms in the initial data. The method of sentinels'' of J. L. Lions [7] is followed to construct a sentinel using the observed vibrations on the boundary. Such a sentinel, by construction, provides information on pollution terms independent of missing terms. This requires resolution of initial-boundary value...
We consider the stabilization of Maxwell’s equations with space-time variable coefficients in a bounded region with a smooth boundary by means of linear or nonlinear Silver–Müller boundary condition. This is based on some stability estimates that are obtained using the “standard” identity with multiplier and appropriate properties of the feedback. We deduce an explicit decay rate of the energy, for instance exponential, polynomial or logarithmic decays are available for appropriate feedbacks.
We consider the stabilization of
Maxwell's equations with space-time variable coefficients
in a bounded region with a smooth boundary
by means of linear or nonlinear Silver–Müller boundary condition.
This is based on some stability estimates
that are obtained using the “standard" identity with multiplier
and appropriate properties of the feedback.
We deduce an explicit decay rate of the energy, for instance
exponential,
polynomial or logarithmic decays are available for appropriate
feedbacks.
...
We propose a direct approach to obtain the boundary stabilization of the isotropic linear elastodynamic system by a natural feedback; this method uses local coordinates in the expression of boundary integrals as a main tool. It leads to an explicit decay rate of the energy function and requires weak geometrical conditions: for example, the spacial domain can be the difference of two star-shaped sets.
The paper presents fractional-order semilinear, continuous, finite-dimensional dynamical systems with multiple delays both in controls and nonlinear function . The constrained relative controllability of the presented semilinear system and corresponding linear one are discussed. New criteria of constrained relative controllability for the fractional semilinear systems with delays under assumptions put on the control values are established and proved. The conical type constraints are considered....
This paper is concerned with complete controllability of a class of nonlinear stochastic systems involving impulsive effects in a finite time interval by means of controls whose initial and final values can be assigned in advance. The result is achieved by using a fixed-point argument.
Recently several papers have related the production of sampling and interpolating sequences for multi-band signals to the solution of certain kinds of Wiener-Hopf equations. Our approach is based on connections between exponential Riesz bases and the controllability of distributed parameter systems. For the case of two-band signals we derive an operator whose invertibility is equivalent to the existence of a sampling and interpolating sequence, and prove the invertibility of this operator.
Recent years have witnessed an increasing interest in coordinated control of distributed dynamic systems. In order to steer a distributed dynamic system to a desired state, it often becomes necessary to have a prior control over the graph which represents the coupling among interacting agents. In this paper, a simple but compelling model of distributed dynamical systems operating over a dynamic graph is considered. The structure of the graph is assumed to be relied on the underling system's states....
A control system of the second order in time with control
is considered. If the
system is controllable in a strong sense and
uT is the control
steering the system to the rest at time
T,
then the L2–norm of uT decreases as
while the –norm of uT is approximately constant.
The proof is based on the moment approach
and properties of the relevant exponential family. Results are
applied to the wave equation with boundary or distributed controls.
We consider a controllability problem for a beam, clamped at one boundary and
free at the other boundary, with an attached piezoelectric actuator. By
Hilbert Uniqueness Method (HUM)
and new results on diophantine approximations, we
prove that the space of exactly initial controllable data depends on the
location of the actuator. We also illustrate these results with numerical
simulations.
A general framework for computing robust controllable sets of
constrained nonlinear uncertain discrete-time systems as well as
controlling such complex systems based on the computed robust
controllable sets is introduced in this paper. The addressed
one-step control approach turns out to be a robust model predictive
control scheme with feasible unit control horizon and contractive
constraint. The solver of 1-dimensional quantified set inversion in
modal interval analysis is extended to 2-dimensional...
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576