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Displaying 901 –
920 of
4417
We consider a class of discrete convex functionals which satisfy a
(generalized) coarea formula. These functionals, based on submodular
interactions, arise in discrete optimization and are known as a large class
of problems which can be solved in polynomial time. In particular, some of
them can be solved very efficiently by maximal flow algorithms and are quite
popular in the image processing community. We study the limit in the continuum
of these functionals, show that they always converge...
The paper is divided in two parts. In the first part a deep investigation is made on some system theoretical aspects of periodic systems and control, including the notions of and norms, the parametrization of stabilizing controllers, and the existence of periodic solutions to Riccati differential equations and/or inequalities. All these aspects are useful in the second part, where some parametrization and control problems in and are introduced and solved.
This paper deals with some state-feedback control problems for continuous time periodic systems. The derivation of the theoretical results underlying such problems has been presented in the first part of the paper. Here, the parametrization and optimization problems in , and mixed are introduced and solved.
In this article we apply the optimal and the robust control theory to the sine-Gordon equation. In our case the control is given by the boundary conditions and we work in a finite time horizon. We present at the beginning the optimal control problem and we derive a necessary condition of optimality and we continue by formulating a robust control problem for which existence and uniqueness of solutions are derived.
In this article we apply the optimal and
the robust control theory to the sine-Gordon equation. In our case
the control is given by the boundary conditions and we work in a finite
time horizon. We present at the beginning the optimal control problem
and we derive a necessary condition of optimality and we continue by
formulating a robust control problem for which existence and uniqueness
of solutions are derived.
Four optimal design problems and a weight minimization problem are considered for elastic plates with small bending rigidity, resting on a unilateral elastic foundation, with inner rigid obstacles and a friction condition on a part of the boundary. The state problem is represented by a variational inequality and the design variables influence both the coefficients and the set of admissible state functions. If some input data are allowed to be uncertain a new method of reliable solutions is employed....
This paper focuses on the analytical properties of the
solutions to the continuity equation with non local flow. Our
driving examples are a supply chain model and an equation for the
description of pedestrian flows. To this aim, we prove the well
posedness of weak entropy solutions in a class of equations
comprising these models. Then, under further regularity conditions,
we prove the differentiability of solutions with respect to the
initial datum and characterize this derivative. A necessary
...
This paper focuses on the analytical properties of the
solutions to the continuity equation with non local flow. Our
driving examples are a supply chain model and an equation for the
description of pedestrian flows. To this aim, we prove the well
posedness of weak entropy solutions in a class of equations
comprising these models. Then, under further regularity conditions,
we prove the differentiability of solutions with respect to the
initial datum and characterize this derivative. A necessary
...
The control of the surface of water in a long canal by means of a wavemaker is investigated. The fluid motion is governed by the Korteweg-de Vries equation in lagrangian coordinates. The null controllability of the elevation of the fluid surface is obtained thanks to a Carleman estimate and some weighted inequalities. The global uncontrollability is also established.
The control of the surface of water in a long canal by
means of a wavemaker is investigated. The fluid motion is governed
by the Korteweg-de Vries equation in Lagrangian coordinates.
The null controllability of the elevation of the fluid surface
is obtained thanks to a Carleman estimate and some weighted inequalities.
The global uncontrollability is also established.
We study an initial boundary-value problem for a wave equation with time-dependent sound speed. In the control problem, we wish to determine a sound-speed function which damps the vibration of the system. We consider the case where the sound speed can take on only two values, and propose a simple control law. We show that if the number of modes in the vibration is finite, and none of the eigenfrequencies are repeated, the proposed control law does lead to energy decay. We illustrate the rich behavior...
We study an initial boundary-value problem for a wave
equation with time-dependent sound speed. In the control problem,
we wish to determine a sound-speed function which damps the
vibration of the system. We consider the case where the sound speed can
take on only two values, and propose a simple control law. We show
that if the number of modes in the vibration is finite, and none of
the eigenfrequencies are repeated, the proposed
control law does lead to energy decay. We illustrate the rich behavior
of...
We wish to show how the shock position in a nozzle could be controlled. Optimal control theory and algorithm is applied to the transonic equation. The difficulty is that the derivative with respect to the shock position involves a Dirac mass. The one dimensional case is solved, the two dimensional one is analyzed .
We wish to show how the shock position in a nozzle could be
controlled. Optimal control theory and algorithm is applied to the
transonic equation. The difficulty is that the derivative with
respect to the shock position involves a Dirac mass. The one
dimensional case is solved, the two dimensional one is analyzed .
We consider optimal control problems for convection-diffusion equations with a pointwise control or a control localized on a smooth manifold. We prove optimality conditions for the control variable and for the position of the control. We do not suppose that the coefficient of the convection term is regular or bounded, we only suppose that it has the regularity of strong solutions of the Navier–Stokes equations. We consider functionals with an observation on the gradient of the state. To obtain optimality...
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