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Displaying 581 –
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687
The present paper studies an optimization problem of dynamically loaded cylindrical tubes. This is a problem of linear elasticity theory. As we search for the optimal thickness of the tube which minimizes the displacement under forces, this is a problem of shape optimization. The mathematical model is given by a differential equation (ODE and PDE, respectively); the mechanical problem is described as an optimal control problem. We consider both the stationary (time independent) and the transient...
The aim of the present paper is to study problems of optimal design in mechanics, whose variational form is given by inequalities expressing the principle of virtual power in its inequality form. The elliptic, linear symmetric operators as well as convex sets of possible states depend on the control parameter. The existence theorem for the optimal control is applied to design problems for an elastic laminated plate whose variable thickness appears as a control variable.
An axisymmetric system of mould, glass piece, plunger and plunger cavity is considered. The state problem is given as a stationary head conduction process. The system includes the glass piece representing the heat source and is cooled inside the plunger cavity by flowing water and outside by the environment of the mould. The design variable is taken to be the shape of the inner surface of the plunger cavity. The cost functional is the second power of the norm in the weighted space of difference...
We minimize, with respect to shape, the moment of inertia of a turbine having the given lowest eigenfrequency of the torsional oscillations. The necessary conditions of optimality in conjunction with certain physical parameters admit a unique optimal design.
We minimize, with respect to shape, the moment of inertia of a
turbine having the given
lowest eigenfrequency of the torsional oscillations. The necessary
conditions of optimality in conjunction with certain
physical parameters admit a unique optimal design.
We deal with an optimal control problem with respect to a variable thickness for a dynamic viscoelastic plate with velocity constraints. The state problem has the form of a pseudohyperbolic variational inequality. The existence and uniqueness theorem for the state problem and the existence of an optimal thickness function are proved.
Slightly below the transition temperatures, the behavior of superconducting materials is governed by the Ginzburg-Landau (GL) equation which characterizes the dynamical interaction of the density of superconducting electron pairs and the exited electromagnetic potential. In this paper, an optimal control problem of the strength of external magnetic field for one-dimensional thin film superconductors with respect to a convex criterion functional is considered. It is formulated as a nonlinear coefficient...
Optimal feedback control depending only on the system state is constructed for a control problem by the non-causal descriptor system for which optimal feedback control depending on state derivatives was considered in the paper (Meuller, 1998). To this end, a non-symmetric solution of the algebraic operator Riccati equation is used.
In this paper, we solve an optimal control problem using the
calculus of variation. The system under consideration is a
switched autonomous delay system that undergoes jumps at the
switching times. The control variables are the instants when the
switches occur, and a set of scalars which determine the jump
amplitudes. Optimality conditions involving analytic expressions
for the partial derivatives of a given cost function with respect
to the control variables are derived using the calculus of
variation....
We consider a linear damped wave equation defined on a two-dimensional domain Ω, with a dissipative term localized in a subset ω. We address the shape design problem which consists in optimizing the shape of ω in order to minimize the energy of the system at a given time T . By introducing an adjoint problem, we first obtain explicitly the (shape) derivative of the energy at time T with respect to the variation in ω. Expressed as a boundary integral on ∂ω, this derivative is then used as an advection...
The Linear-Quadratic (LQ) optimal control problem is studied for a
class of first-order hyperbolic partial differential equation models
by using a nonlinear infinite-dimensional (distributed parameter) Hilbert state-space
description. First the dynamical properties of the linearized model
around some equilibrium profile are studied. Next the LQ-feedback
operator is computed by using the corresponding operator Riccati
algebraic equation whose solution is obtained via a related
matrix Riccati differential...
We study the Monge transportation problem when the cost is the action associated to
a Lagrangian function on a compact manifold. We show that the transportation can be interpolated by a Lipschitz lamination. We describe several direct variational problems the minimizers of
which are these Lipschitz laminations. We prove the existence of an optimal transport map when the transported measure is absolutely continuous. We explain the relations with Mather’s minimal measures.
We study the potential which minimizes the fundamental gap of the
Schrödinger operator under the total mass constraint. We consider
the relaxed potential and prove a regularity result for the optimal
one, we also give a description of it. A consequence of this result
is the existence of an optimal potential under L1 constraints.
A multiphase generalization of the Monge–Kantorovich optimal transportation problem is addressed. Existence of optimal solutions is established. The optimality equations are related to classical Electrodynamics.
A multiphase generalization of the Monge–Kantorovich optimal
transportation problem is addressed.
Existence of optimal solutions is established.
The optimality equations are related to classical Electrodynamics.
A continuous version of optimal LQG design under presence of Wiener disturbances is solved for MIMO controlled plant. Traditional design tools fail to solve this problem due to unstability of the augmented plant. A class of all optimality criteria, which guarantee existence of an asymptotical solution, is defined using a plant deviation model. This class is utilized in design of an optimal state and an error feedback regulator which is presented here. The resultant optimal error regulator is interpreted...
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