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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.
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....
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...
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...
In this paper we deepen the study of the nonlinear principal components introduced by Salinelli in 1998, referring to a real random variable. New insights on their probabilistic and statistical meaning are given with some properties. An estimation procedure based on spline functions, adapting to a statistical framework the classical Rayleigh–Ritz method, is introduced. Asymptotic properties of the estimator are proved, providing an upper bound for the rate of convergence under suitable mild conditions....
We prove partial regularity with optimal Hölder exponent of
vector-valued minimizers u of the quasiconvex variational integral under polynomial growth. We employ the indirect
method of the bilinear form.
In this paper, we investigate the optimal location of secondary sources (controls) to enhance the reduction of the noise field in a one-dimensional acoustic cavity. We first formulate the active control strategy as a linear quadratic tracking (LQT) problem in a Hilbert space, and then formulate the optimization problem as minimizing an appropriate performance criterion based on the LQT cost function with respect to the location of the controls. A numerical scheme based on the Legendre–tau method...
We consider the dynamic control problem of attaining a target position at a finite time T, while minimizing a linear-quadratic cost functional depending on the position and speed. We assume that the coefficients of the linear-quadratic cost functional are stochastic processes adapted to a Brownian filtration. We provide a probabilistic solution in terms of two coupled backward stochastic differential equations possessing a singularity at the terminal time T. We verify optimality of the candidate...
In the paper there is discussed a problem of the resource allocation in a large scale system in the presence of the resource shortages. The control task is devided into two levels, with the coordinator on the upper level and local controllers on the lower one. It is assumed that they have different information. The coordinator has an information on mean values of users demands, an inflow forecast and an estimation of the resource amount in a storage reservoir. On the basis on this information it...
Some necessary and some sufficient conditions are established for the explicit construction and characterization of optimal solutions of multivariate transportation (coupling) problems. The proofs are based on ideas from duality theory and nonconvex optimization theory. Applications are given to multivariate optimal coupling problems w.r.t. minimal -type metrics, where fairly explicit and complete characterizations of optimal transportation plans (couplings) are obtained. The results are of interest...
In the paper the problem of constructing an optimal urban transportation network in a city with given densities of population and of workplaces is studied. The network is modeled by a closed connected set of assigned length, while the optimality condition consists in minimizing the Monge-Kantorovich functional representing the total transportation cost. The cost of trasporting a unit mass between two points is assumed to be proportional to the distance between them when the transportation is carried...
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380 of
598