Equations In Real Time Research Articles

A recurrent neural network for solving linear projection equations

Linear projection equations arise in many optimization problems and have important applications in science and engineering. In this paper, we present a recurrent neural network for solving linear projection equations in real time. The proposed neural network has two layers and is amenable to parallel implementation with simple hardware. In the theoretical aspect, we prove that the proposed neural network can converge globally to the solution set of the problem when the matrix involved in the problem is positive semidefinite and can converge exponentially to a unique solution when the matrix is positive definite. In addition, we analyze the stability of the related dynamic system in detail. As an application, we show that the proposed neural network can be used directly to solve linear and convex quadratic programming problems and linear complementary problems with positive semidefinite matrices. The validity and transient behavior of the neural network are demonstrated by using three numerical examples.

On the Synthesis Problem for Optimal Control Systems

A new approach to the synthesis problem of optimal controls of feedback type is considered. Algorithms of operating optimal controllers which are able to calculate values of optimal feedbacks during each particular control process in real time are described. The algorithm of operating the controller of the first type (continuous controller) is based on solving special (defining) equations in real time using the Newton method. For operating the optimal controller of the second type (discrete controller) the dual method of linear programming is used. In control problems for systems under uncertainty, a nonstochastic model is used, around which guaranteed results are obtained. Under incomplete and inexact information, problems of optimal observation and identification are introduced. Algorithms of operating the optimal estimator and identifier which are able to construct estimates of available information required for operating the optimal output controller in real time are described. Results are illustrated by optimization problems of the fourth order control system.

Fermion damping in a fermion-scalar plasma

In this article we study the dynamics of fermions in a fermion-scalar plasma. We begin by obtaining the effective in-medium Dirac equation in real time which is fully renormalized and causal and leads to the initial value problem. For a heavy scalar we find the novel result that the decay of the scalar into fermion pairs in the medium leads to damping of the fermionic excitations and their in-medium propagation as quasiparticles. That is, the fermions acquire a width due to the decay of the heavier scalar in the medium. We find the damping rate to lowest order in the Yukawa coupling for arbitrary values of scalar and fermion masses, temperature and fermion momentum. An all-order expression for the damping rate in terms of the exact quasiparticle wave functions is established. A kinetic Boltzmann approach to the relaxation of the fermionic distribution function confirms the damping of fermionic excitations as a consequence of the induced decay of heavy scalars in the medium. A linearization of the Boltzmann equation near equilibrium clearly displays the relationship between the damping rate of fermionic mean fields and the fermion interaction rate to lowest order in the Yukawa coupling directly in real time.

A multilayer recurrent neural network for solving continuous-time algebraic Riccati equations

A multilayer recurrent neural network is proposed for solving continuous-time algebraic matrix Riccati equations in real time. The proposed recurrent neural network consists of four bidirectionally connected layers. Each layer consists of an array of neurons. The proposed recurrent neural network is shown to be capable of solving algebraic Riccati equations and synthesizing linear-quadratic control systems in real time. Analytical results on stability of the recurrent neural network and solvability of algebraic Riccati equations by use of the recurrent neural network are discussed. The operating characteristics of the recurrent neural network are also demonstrated through three illustrative examples.

Quantum transport and non-linear dynamics of interacting quantized fields and applications to nanoelectronics and optoelectronics

A non-equilibrium dynamics of interacting quantized fields based on the Liouville space quantum field dynamics is outlined here. The self-consistent treatment of quantum transport given here expresses the theory in terms of renormalized propagators and renormalized many-body interactions. The quantum transport equation for the particle quantum distribution function is extracted from the general equation in real time for each particle species in a system consisting of several components. Although it is equivalent to the so-called non-equilibrium Green's function theory of Schwinger and Keldysh, it has several technical advantages. We suggest a method to implement numerically the self-consistent scheme by generalizing the many-body functional methods (e.g. the density functional techniques) in condensed matter physics to highly non-equilibrium situations. Several important problems in nanoelectronics and optoelectronics where this formalism is essential are mentioned.

A Time-integration Method Using Artificial Compressibility For Unsteady Viscous Flows

A time-accurate integration method for the study of unsteady incompressible viscous flows is presented, based on a three-point-backward implicit discretization of the Navier-Stokes equations in real time and a pseudo-time relaxation with artificial compressibility to advance the solution between consecutive real time levels. The spatial discretization uses central differencing based on a stretched staggered grid. A factored ADI scheme with lagged non-linearities is used to reduce the problem to the solution of scalar tridiagonal systems. This method displays very good computing efficiency and accuracy when applied for validation to several typical steady and unsteady flow problems.

HAMILTONIAN DYNAMICS OF YANG-MILLS FIELDS ON A LATTICE

We review recent results from studies of the dynamics of classical Yang-Mills fields on a lattice. We discuss the numerical techniques employed in solving the classical lattice Yang-Mills equations in real time, and present results exhibiting the universal chaotic behavior of non-abelian gauge theories. The complete spectrum of Lyapunov exponents is determined for the gauge group SU(2). We survey results obtained for the SU(3) gauge theory and other nonlinear field theories. We also discuss the relevance of these results to the problem of thermalization in gauge theories.

Simplified neural networks for solving linear least squares and total least squares problems in real time

In this paper a new class of simplified low-cost analog artificial neural networks with on chip adaptive learning algorithms are proposed for solving linear systems of algebraic equations in real time. The proposed learning algorithms for linear least squares (LS), total least squares (TLS) and data least squares (DLS) problems can be considered as modifications and extensions of well known algorithms: the row-action projection-Kaczmarz algorithm and/or the LMS (Adaline) Widrow-Hoff algorithms. The algorithms can be applied to any problem which can be formulated as a linear regression problem. The correctness and high performance of the proposed neural networks are illustrated by extensive computer simulation results.

Solving simultaneous linear equations using recurrent neural networks

Simultaneous linear algebraic equations can be found in many mathematical model formulations. In monitoring and control of dynamic systems, there is often a need for solving simultaneous linear algebraic equations in real time. In this paper, recurrent neural networks for solving simultaneous linear algebraic equations are proposed. The asymptotic stability of the proposed neural networks and solvability of simultaneous linear equations by using the neural networks are substantiated. A circuit schematic for realizing the neural networks is described. The results of numerical simulations are discussed via illustrative examples. An extension of the recurrent neural networks for solving quadratic programming problems subject to equality constraints is also discussed.

Nonperturbative evaluation of the diffusion rate in field theory at high temperatures.

Kramer's approach to the rate of the thermally activated escape from a metastable state is extended to field theory. Diffusion rate in the 1+1-dimensional Sine-Gordon model as a function of temperature and friction coefficient is evaluated numerically by solving the Langevin equation in real time. A clear crossover from the semiclassical to the high temperature domain is observed. The temperature behaviour of the diffusion rate allows one to determine the kink mass which is found equal to the corresponding classical value. The Kramer's predictions for the dependence on viscosity are qualitatively valid in this multidimensional case. In the limit of vanishing friction the diffusion rate is shown to coincide with the one obtained from the direct measurements of the conventional classical real-time Green function at finite temperature.

On the diffusion in the Sine-Gordon field theory at high temperatures

Diffusion rate in the 1 + 1-dimensional Sine-Gordon field theory as a function of temperature and friction coefficient is evaluated numerically by solving the Langevin equation in real time. A clear crossover from the semiclassical to the high temperature domain is observed. The temperature behaviour of the diffusion rate allows one to determine the kink mass which is found equal to the corresponding classical value. The Kramer's predictions for the dependence on viscosity are qualitatively valid in this multidimensional case. In the limit of vanishing friction the diffusion rate is shown to coincide with the one obtained from the direct measurements of the conventional classical real-time Green function at finite temperature.

Nonlinear process simulation and control using transputers

One of the obstacles to the more extensive use of nonlinear models in the control of highly nonlinear systems, such as chemical processing equipment, is the computational difficulty of solving the relevant nonlinear differential algebraic equations in real time. Transputer systems offer sufficient power to enable these equations to be handled rapidly and are now cheap enough to enable their implementation as dedicated control room equipment to be considered. Feedforward/feedback control of a nonlinear process, a distillation column, has been simulated on a Meiko transputer system to demonstrate the feasibility of this approach. The effective use of parallel computers requires that parallelism be exploited by choice of problem decomposition. A strategy which maximises parallelisation in the simulation of a distillation column is described.

Topological transitions at finite temperatures: A real time numerical approach

We study topological transitions at finite temperatures within the (1 + 1)-dimensional abelian Higgs model by a numerical simulation in real time. Basic ideas of the real-time approach are presented and some peculiarities of the Metropolis technique are discussed. It is argued that the processes leading to topological transitions are of classical origin; the transitions can be observed by solving the classical field equations in real time. We show that the topological transitions actually pass via the sphaleron configuration. The transition rate as a function of temperature is found to be in good agreement with the analytical predictions. No extra suppression of the rate is observed. The conditions of applicability of our approach are discussed. The temperature interval where the low-temperature broken phase persists is estimated.

Real-time adaptive controllers for a turbine generator

The design and practical application of series-parallel model following adaptive control techniques to a turbogenerator system is described, incorporating proportional-plus-integral and relay-plus-integral adaptation laws. An advantage of this scheme is that it does not require on-line identification, nor the solution of linear or non-linear equations in real time. The aim is to generate an adaptive command signal, such that the output of the turbogenerator will match the output of the model, even when the system is subjected to output disturbances or changes in operating conditions. The turbogenerator system consists of a synchronous generator connected to an infinite busbar through a transformer and two transmission lines in parallel. The control scheme has been thoroughly tested on a micromachine system, over a wide range of operating conditions. Typical simulation and experimental results are presented, illustrating the response to a short-circuit on the transmission network, and including comparison with a fixed-gain optimal controller. These show that the adaptive controllers are most effective, providing rapid convergence of the turbogenerator and model outputs, and an improved performance.

Sphaleron transitions at finite temperatures. numerical study in (1+1) dimensions

Finite temperature sphaleron transitions in (1+1)-dimensional abelian Higgs model are studied numerically. It is argued that thermal transitions can be investigated from first principles by solving the classical field equations in real time. We find that the sphaleron mechanism is adequate and the transition rate is consistent with the Boltzmann law. No extra suppression of the rate is observed.

Adaptive Control of Alumina Reduction Cells with Pointfeeders

Cood alumina feeding control is important to obtain optimum cell operation. Cells with pointfceders may successfully be operated within narrow ranges of alumina concentration in the bath, to reduce anode effect frequency and stabilize cell operation. Control of an alumina reduction cell is difficult due to the lack of measurements which may give information about the internal state of the cell. Normally the only on-line measurement is the resistance of the cell, or more correctly the current and the voltage. ÅSV has developed an adaptiv controller to get as much information as possible from the resistance. The adaptive controller uses the Maximum Likelihood method for estimation of the process parameters. In ÅSV we have more than 1200 reduction cells. We are now installing one micromputer pr. cell. The microcomputer is developed by ÅSV. We have done this because we did not find any microcomputer in the market that satisfied our requirements. Our microcomputer is designed to operate in potroom conditions. The microcomputer is equiped with Intel 8086 microprocessor and a numeric dataprocessor, Intel 8087. This combination are running all the adaptive controller equations in real time. The results achived with adaptive controllers and microcomputers are very good. We have reached current efficencies of 94 - 95 % and energy consumption of 13.2 kWh/kg Al.