Exact penalties for variational inequalities with applications to nonlinear complementarity problems

In this paper, we present a new reformulation of the KKT system associated to a variational inequality as a semismooth equation. The reformulation is derived from the concept of differentiable exact penalties for nonlinear programming. The best theoretical results are presented for nonlinear complementarity problems, where simple, verifiable, conditions ensure that the penalty is exact. We close the paper with some preliminary computational tests on the use of a semismooth Newton method to solve the equation derived from the new reformulation. We also compare its performance with the Newton method applied to classical reformulations based on the Fischer-Burmeister function and on the minimum. The new reformulation combines the best features of the classical ones, being as easy to solve as the reformulation that uses the Fischer-Burmeister function while requiring as few Newton steps as the one that is based on the minimum.

Stability and Hopf bifurcation in an hexagonal governor system

In this paper we study the Lyapunov stability and the Hopf bifurcation in a system coupling an hexagonal centrifugal governor with a steam engine. Here are given sufficient conditions for the stability of the equilibrium state and of the bifurcating periodic orbit. These conditions are expressed in terms of the physical parameters of the system, and hold for parameters outside a variety of codimension two. (C) 2007 Elsevier Ltd. All rights reserved.

Residual-based test for Nonlinear Cointegration with application in PPPs

Nested by linear cointegration first provided in Granger (1981), the definition of nonlinear cointegration is presented in this paper. Sequentially, a nonlinear cointegrated economic system is introduced. What we mainly study is testing no nonlinear cointegration against nonlinear cointegration by residual-based test, which is ready for detecting stochastic trend in nonlinear autoregression models. We construct cointegrating regression along with smooth transition components from smooth transition autoregression model. Some properties are analyzed and discussed during the estimation procedure for cointegrating regression, including description of transition variable. Autoregression of order one is considered as the model of estimated residuals for residual-based test, from which the teststatistic is obtained. Critical values and asymptotic distribution of the test statistic that we request for different cointegrating regressions with different sample sizes are derived based on Monte Carlo simulation. The proposed theoretical methods and models are illustrated by an empirical example, comparing the results with linear cointegration application in Hamilton (1994). It is concluded that there exists nonlinear cointegration in our system in the final results.

Testing common nonlinear features in vector nonlinear autoregressive models

This paper studies a special class of vector smooth-transition autoregressive (VSTAR) models that contains common nonlinear features (CNFs), for which we proposed a triangular representation and developed a procedure of testing CNFs in a VSTAR model. We first test a unit root against a stable STAR process for each individual time series and then examine whether CNFs exist in the system by Lagrange Multiplier (LM) test if unit root is rejected in the first step. The LM test has standard Chi-squared asymptotic distribution. The critical values of our unit root tests and small-sample properties of the F form of our LM test are studied by Monte Carlo simulations. We illustrate how to test and model CNFs using the monthly growth of consumption and income data of United States (1985:1 to 2011:11).

Tayloring Brazil: a system dynamics model for monetary policy feedback

The thesis introduces a system dynamics Taylor rule model of new Keynesian nature for monetary policy feedback in Brazil. The nonlinear Taylor rule for interest rate changes con-siders gaps and dynamics of GDP growth and inflation. The model closely tracks the 2004 to 2011 business cycle and outlines the endogenous feedback between the real interest rate, GDP growth and inflation. The model identifies a high degree of endogenous feedback for monetary policy and inflation, while GDP growth remains highly exposed to exogenous eco-nomic conditions. The results also show that the majority of the monetary policy moves during the sample period was related to GDP growth, despite higher coefficients of inflation parameters in the Taylor rule. This observation challenges the intuition that inflation target-ing leads to a dominance of monetary policy moves with respect to inflation. Furthermore, the results suggest that backward looking price-setting with respect to GDP growth has been the dominant driver of inflation. Moreover, simulation exercises highlight the effects of the new BCB strategy initiated in August 2011 and also consider recession and inflation avoid-ance versions of the Taylor rule. In methodological terms, the Taylor rule model highlights the advantages of system dynamics with respect to nonlinear policies and to the stock-and-flow approach. In total, the strong historical fit and some counterintuitive observations of the Taylor rule model call for an application of the model to other economies.

Weed interference on maize (Zea mays) under no tillage system

A field trial was carried out in Brazil in March 2002 with the aim to evaluate the effects of different timing and extension of weedy period on maize productivity. The hybrid Pioneer 30K75 was sowed under 7 t ha(-1) mulching promoted by glyphosate spraying. The treatments were divided in two groups: In the first group, weeds were maintained since the maize sowing until different periods in the crop cycle: 0, 14, 28, 42, 56, 70, and 150 days (harvesting time). In the second group, the maize crop was kept weed free for the same periods of the first group. Weed control was done through hand hoeing. A complete randomized blocks experimental design with five replications was used for plots distribution in the field. Nonlinear regression model was used to study the effects of weedy or weedfree periods on maize productivity. Weed community included 13 families and 31 species. Asteraceae, Poaceae, and Euphorbiaceae were the most abundant families. Results showed that under no tillage condition with 7 t ha-1 mulching at sowing time, the maize crop could cohabit with weed community for 54 days without any yield lost. on the other hand, if the crop was kept weed free for 27 days, the weed interference was not enable to reduce maize production. According to these results one weed control measure between 27 and 54 days after crop emergence could be enough to avoid any reduction in maize productivity.

Global dynamics of the Rikitake system

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Allocation of protective devices in distribution circuits using nonlinear programming models and genetic algorithms

The optimized allocation of protective devices in strategic points of the circuit improves the quality of the energy supply and the system reliability index. This paper presents a nonlinear integer programming (NLIP) model with binary variables, to deal with the problem of protective device allocation in the main feeder and all branches of an overhead distribution circuit, to improve the reliability index and to provide customers with service of high quality and reliability. The constraints considered in the problem take into account technical and economical limitations, such as coordination problems of serial protective devices, available equipment, the importance of the feeder and the circuit topology. The use of genetic algorithms (GAs) is proposed to solve this problem, using a binary representation that does (1) or does not (0) show allocation of protective devices (reclosers, sectionalizers and fuses) in predefined points of the circuit. Results are presented for a real circuit (134 busses), with the possibility of protective device allocation in 29 points. Also the ability of the algorithm in finding good solutions while improving significantly the indicators of reliability is shown. (C) 2003 Elsevier B.V. All rights reserved.

A Constructive Heuristic Algorithm for Distribution System Planning

A constructive heuristic algorithm (CHA) to solve distribution system planning (DSP) problem is presented. The DSP is a very complex mixed binary nonlinear programming problem. A CHA is aimed at obtaining an excellent quality solution for the DSP problem. However, a local improvement phase and a branching technique were implemented in the CHA to improve its solution. In each step of the CHA, a sensitivity index is used to add a circuit or a substation to the distribution system. This sensitivity index is obtained by solving the DSP problem considering the numbers of circuits and substations to be added as continuous variables (relaxed problem). The relaxed problem is a large and complex nonlinear programming and was solved through an efficient nonlinear optimization solver. Results of two tests systems and one real distribution system are presented in this paper in order to show the ability of the proposed algorithm.

Imposing Radiality Constraints in Distribution System Optimization Problems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Force and displacement transmissibility of a nonlinear isolator with high-static-low-dynamic-stiffness

Engineers often face the challenge of reducing the level of vibrations experienced by a given payload or those transmitted to the support structure to which a vibrating source is attached. In order to increase the range over which vibrations are isolated, soft mounts are often used in practice. The drawback of this approach is the static displacement may be too large for reasons of available space for example. Ideally, a vibration isolator should have a high-static stiffness, to withstand static loads without too large a displacement, and at the same time, a low dynamic stiffness so that the natural frequency of the system is as low as possible which will result in an increased isolation region. These two effects are mutually exclusive in linear isolators but can be overcome if properly configured nonlinear isolators are used. This paper is concerned with the characterisation of such a nonlinear isolator comprising three springs, two of which are configured to reduce the dynamic stiffness of the isolator. The dynamic behaviour of the isolator supporting a lumped mass is investigated using force and displacement transmissibility, which are derived by modelling the dynamic system as a single-degree-of-freedom system. This results in the system dynamics being approximately described by the Duffing equation. For a linear isolator, the dynamics of the system are the same regardless if the source of the excitation is a harmonic force acting on the payload (force transmissibility) or a harmonic motion of the base (displacement transmissibility) on which the payload is mounted. In this paper these two expressions are compared for the nonlinear isolator and it is shown that they differ. A particular feature of the displacement transmissibility is that the response is unbounded at the nonlinear resonance frequency unless the damping in the isolator is greater than some threshold value, which is not the case for force transmissibility. An explanation for this is offered in the paper. (C) 2011 Elsevier Ltd. All rights reserved.

On an Optimal Linear Control of a Chaotic Non-Ideal Duffing System

In this work, we use a nonlinear control based on Optimal Linear Control. We used as mathematical model a Duffing equation to model a supporting structure for an unbalanced rotating machine with limited power (non-ideal motor). Numerical simulations are performed for a set control parameter (depending on the voltage of the motor, that is, in the static and dynamic characteristic of the motor) The interaction of the non-ideal excitation with the structure may lead to the occurrence of interesting phenomena during the forward passage through the several resonance states of the system. Chaotic behavior is obtained for values of the parameters. Then, the proposed control strategy is applied in order to regulate the chaotic behavior, in order to obtain a periodic orbit and to decrease its amplitude. Both methodologies were used in complete agreement between them. The purpose of the paper is to give suggestions and recommendations to designers and engineers on how to drive this kind of system through resonance.

Control aspects in nonlinear Hill's equation

The Hill's equations-even in the linear original version are a describer of phenomenon having chaotic flavor, giving sometimes very unusual situations. The theory of the so called intervals of instability in the equation provides the precise description for most of these phenomena. Considerations on nonlinearities into the Hill's equation is a quite recent task. The linearized version for almost of these systems it reduces to the Hill's classical linear one. In this paper, some indicative facts are pointed out on the possibility of having the linear system stabilizable and/or exactly controllable. As consequence of such an approach we get results having strong classical aspects, like the one talking about location of parameters in intervals of stability. A result for nonlinear proper periodic controls, is considered too. (C) 2010 Elsevier B.V. All rights reserved.

Control Design Applied to a Micro Electro Mechanical System: MEMS Comb drive

This paper presents the linear optimal control technique for reducing the chaotic movement of the micro-electro-mechanical Comb Drive system to a small periodic orbit. We analyze the non-linear dynamics in a micro-electro-mechanical Comb Drive and demonstrated that this model has a chaotic behavior. Chaos control problems consist of attempts to stabilize a chaotic system to an equilibrium point, a periodic orbit, or more general, about a given reference trajectory. This technique is applied in analyzes the nonlinear dynamics in an MEMS Comb drive. The simulation results show the identification by linear optimal control is very effective.