Search results for "Control variable"
showing 7 items of 17 documents
Optimization of two-step batch processes and the method of compensation for random error
2012
This paper considers the problem of the optimal setting of controllable variables in two-step processes with quality constraints. The optimal setting minimizes the cost and satisfies quality constraints defined for the final output. The main emphasis is given to processes where it is possible to make intermediate measurements after the first processing step and to utilize these measurements before the control variables in the second step are set. Optimization based on this method of compensation for random error can yield substantially lower cost than does optimization based on a strategy where all variables are fixed before the process starts. An example of application of the method is tak…
Necessary and sufficient conditions for frequency entrainment of quasi-sinusoidal injection-synchonised oscillators
1986
A method is presented which permits the first-approximation exact analysis of the dynamical stability of fundamental-mode injectionsynchronized oscillators (FISO's) characterized by a quasi-sinusoidal quasi-static behavior. By combining small parameter and stroboscopic transformation techniques, the phase-lock stability investigation of an nth-order system is reduced to the simple Hurwitz test on an nth degree polynomial easily obtainable from steady state describing quantities. On this basis, equations for critical locking are also derived, which demonstrate the existence of a pair of limit curves (Locus and Boundary) already conjectured and looked for in the past, but only with partial su…
Contact Shape Optimization
1995
Shape optimization is a branch of the optimal control theory in which the control variable is connected with the geometry of the problem. The aim is to find a shape from an a priori defined class of domains, for wich the corresponding cost functional attains its minimum. Shape optimization of mechanical systems, behaviour of which is described by equations, has been very well analyzed from the mathematical, as well as from the mechanical point of view, see [1], [2], [3] and references therein. The aim of this contribution is to extend results to the case, in which the system is described by the so called variational inequalities. There are two reasons for doing that: 1) The behavior of many…
Gradient with respect to nodes for non-isoparametric finite elements
2006
We consider the problem of controlling the solution of a finite element model using the nodal co-ordinates as control variables. The main emphasis is on the study of the applicability of the domain deformation method for different element types. The results are applied to a simple problem of finite element grid optimization.
Solving some optimal control problems using the barrier penalty function method
2005
In this paper we present a new approach to solve the two-level optimization problem arising from an approximation by means of the finite element method of optimal control problems governed by unilateral boundary value problems. The minimized functional depends on control variables and state variables x. The latter are the optimal solution of an auxiliary quadratic programming problem, whose parameters depend on u.
Optimization of conducting structures by using the homogenization method
2002
Approximation and numerical realization of a class of optimization problems with control variables represented by coefficients of linear elliptic state equations is considered. Convergence analysis of well-posed problems is performed by using one- and two-level approximation strategies. The latter is utilized in an optimization layout problem for two conductive constituents, for which the necessary steps to transfer the well-posed problem into a computational form are described and some numerical experiments are given.
The use of energies as a tool to stabilise climate and world population
2021
It is a fact that population and average global temperature on Earth grow fast. Literature shows that many studies have been performed about it. Nevertheless, forecasts are not good. Assuming that the key implied factors are the consumption of energy (from the different types of energy sources) and the birth rate, we suggest in this research, as a first step, to state a stochastic demographic model, including the necessary and adequate economic, environmental and wellbeing variables. This model will be able to optimise, by means of a genetic algorithm, the amount and proportion of the main source types energy consumption as well as the average birth rate in the world, in order to maintain t…