Optimal control problems with a continuous inequality constraint on the state and the control

We consider an optimal control problem with a nonlinear continuous inequality constraint. Both the state and the control are allowed to appear explicitly in this constraint. By discretizing the control space and applying a novel transformation, a corresponding class of semi-infinite programming problems is derived. A solution of each problem in this class furnishes a suboptimal control for the original problem. Furthermore, we show that such a solution can be computed efficiently using a penalty function method. On the basis of these two ideas, an algorithm that computes a sequence of suboptimal controls for the original problem is proposed. Our main result shows that the cost of these suboptimal controls converges to the minimum cost. For illustration, an example problem is solved. © 2009 Elsevier Ltd. All rights reserved.link_to_subscribed_fulltex

An exact penalty method for free terminal time optimal control problem with continuous inequality constraints

In this paper, we consider a class of optimal control problems with free terminal time and continuous inequality constraints. First, the problem is approximated by representing the control function as a piecewise-constant function. Then the continuous inequality constraints are transformed into terminal equality constraints for an auxiliary differential system. After these two steps, we transform the constrained optimization problem into a penalized problem with only box constraints on the decision variables using a novel exact penalty function. This penalized problem is then solved by a gradient-based optimization technique. Theoretical analysis proves that this penalty function has continuous derivatives, and for a sufficiently large and finite penalty parameter, its local minimizer is feasible in the sense that the continuous inequality constraints are satisfied. Furthermore, this local minimizer is also the local minimizer of the constrained problem. Numerical simulations on the range maximization for a hypersonic vehicle reentering the atmosphere subject to a heating constraint demonstrate the effectiveness of our method

Estudo da curva de crescimento de animais da raça Guzerá e seus cruzamentos alimentados a pasto, com e sem suplementação: 2. Avaliação dos parâmetros da curva de crescimento Growth curve analysis of Guzera and their crossbreds fed under grazing with or without supplementation: 2. Evaluation of growth curve parameters

Este trabalho analisou os parâmetros da função não-linear de Gompertz para descrever o crescimento de machos e fêmeas da raça Guzerá e seus cruzamentos (3/4Guzerá - 1/4Pardo Suíço, 1/2Nelore - 1/4Pardo Suíço - 1/4Guzerá, 1/2Pardo Suíço-1/2Guzerá, 1/2Chianina - 1/4Pardo Suíço - 1/4Guzerá, 1/2Caracú - 1/2Guzerá, 1/2Caracú - 1/4Pardo Suíço - 1/4Guzerá) submetidos a três níveis de suplementação (sem suplementação, suplementação durante o período seco e suplementação durante o ano todo), a fim de verificar as causas de variação nos parâmetros. Existiu interação positiva entre níveis de suplementação e grupo racial e entre grupo racial e sexo para peso adulto e taxa de maturidade. Notou-se também interação entre níveis de suplementação e sexo para a taxa de maturidade e para o parâmetro de integração. Observou-se efeito significativo apenas de grupo racial no parâmetro de integração. A suplementação apenas no período seco não alterou a estimativa do peso adulto. Quando os animais receberam suplementação mais energética, a taxa de maturidade foi aumentada. Os animais que receberam suplementação durante o ano todo apresentaram menor peso adulto e maior taxa de maturidade. As fêmeas prenhas obtiveram maior peso adulto e menor taxa de maturidade. Uma equação alométrica (r² = 0,68) foi derivada para predizer taxa de maturidade a partir do peso adulto.<br>This paper evaluated the parameters of Gompertz nonlinear function to describe Guzera male and female growth curve, and their crossbreds (3/4Guzera - 1/4Brown Swiss, 1/2Nellore - 1/4Brown Swiss - 1/4Guzera, 1/2Brown Swiss - 1/2Guzera, 1/2Chianina - 1/4Brown Swiss - 1/4Guzera, 1/2Caracu - 1/2Guzera, 1/2Caracu - 1/4Brown Swiss - 1/4Guzera) submitted to three levels of supplementation: without supplementation, supplementation only during the dry season, and year-round supplementation. There were significant interactions between supplementation and breed, and breed and sex on mature weight and maturing rate; supplementation and sex on maturing rate and integration parameter; and breed effect on integration parameter. The dry season supplementation did not change mature weight. Increasing the energy content of the supplement increased the maturing rate estimates. Supplementation during year-round decreased the estimates of mature weight but increased maturing rate values. Calving status had a significant effect on mature weight and maturing rate estimates. An allometric equation with an r² of 0.68 was derived to predict maturing rate from mature weight estimates

Point of care HbA1c level for diabetes mellitus management and its accuracy among tuberculosis patients: a study in four countries

BACKGROUND: Diabetes mellitus (DM) is common among tuberculosis (TB) patients and often undiagnosed or poorly controlled. We compared point of care (POC) with laboratory glycated haemoglobin (HbA1c) testing among newly diagnosed TB patients to assess POC test accuracy, safety and acceptability in settings in which immediate access to DM services may be difficult. METHODS: We measured POC and accredited laboratory HbA1c (using high-performance liquid chromatography) in 1942 TB patients aged 18 years recruited from Peru, Romania, Indonesia and South Africa. We calculated overall agreement and individual variation (mean ± 2 standard deviations) stratified by country, age, sex, body mass index (BMI), HbA1c level and comorbidities (anaemia, human immunodeficiency virus [HIV]). We used an error grid approach to identify disagreement that could raise significant concerns. RESULTS: Overall mean POC HbA1c values were modestly higher than laboratory HbA1c levels by 0.1% units (95%CI 0.1–0.2); however, there was a substantial discrepancy for those with severe anaemia (1.1% HbA1c, 95%CI 0.7–1.5). For 89.6% of 1942 patients, both values indicated the same DM status (no DM, HbA1c <6.5%) or had acceptable deviation (relative difference <6%). Individual agreement was variable, with POC values up to 1.8% units higher or 1.6% lower. For a minority, use of POC HbA1c alone could result in error leading to potential overtreatment (n = 40, 2.1%) or undertreatment (n = 1, 0.1%). The remainder had moderate disagreement, which was less likely to influence clinical decisions. CONCLUSION: POC HbA1c is pragmatic and sufficiently accurate to screen for hyperglycaemia and DM risk among TB patients