Optimal growth in a two-sector model without discounting: a geometric investigation

We characterize optimal policy in a two-sector growth model with xed coeÆcients and with no discounting. The model is a specialization to a single type of machine of a general vintage capital model originally formulated by Robinson, Solow and Srinivasan, and its simplicity is not mirrored in its rich dynamics, and which seem to have been missed in earlier work. Our results are obtained by viewing the model as a specific instance of the general theory of resource allocation as initiated originally by Ramsey and von Neumann and brought to completion by McKenzie. In addition to the more recent literature on chaotic dynamics, we relate our results to the older literature on optimal growth with one state variable: speci cally, to the one-sector setting of Ramsey, Cass and Koopmans, as well as to the two-sector setting of Srinivasan and Uzawa. The analysis is purely geometric, and from a methodological point of view, our work can be seen as an argument, at least in part, for the rehabilitation of geometric methods as an engine of analysis.

Security constrained optimal active power flow via network model and interior point method

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

HOW TO EFFICIEN TLY INCORPORATE FACTS DEVICES IN OPTIMAL ACTIVE POWER FLOW MODEL

This paper presents for the first time how to easily incorporate facts devices in an optimal active power flow model such that an efficient interior-point method may be applied. The optimal active power flow model is based on a network flow approach instead of the traditional nodal formulation that allows the use of an efficiently predictor-corrector interior point method speed up by sparsity exploitation. The mathematical equivalence between the network flow and the nodal models is addressed, as well as the computational advantages of the former considering the solution by interior point methods. The adequacy of the network flow model for representing facts devices is presented and illustrated on a small 5-bus system. The model was implemented using Matlab and its performance was evaluated with the 3,397-bus and 4,075-branch Brazilian power system which show the robustness and efficiency of the formulation proposed. The numerical results also indicate an efficient tool for optimal active power flow that is suitable for incorporating facts devices.

On non-linear dynamics and an optimal control synthesis of the action potential of membranes (ideal and non-ideal cases) of the Hodgkin-Huxley (HH) mathematical model

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A model for optimal chemical control of leaf area damaged by fungi population - Parameter dependence

We present a model to study a fungi population submitted to chemical control, incorporating the fungicide application directly into the model. From that, we obtain an optimal control strategy that minimizes both the fungicide application (cost) and leaf area damaged by fungi population during the interval between the moment when the disease is detected (t = 0) and the time of harvest (t = t(f)). Initially, the parameters of the model are considered constant. Later, we consider the apparent infection rate depending on the time (and the temperature) and do some simulations to illustrate and to compare with the constant case.

A mixed-integer LP model for the optimal allocation of voltage regulators and capacitors in radial distribution systems

This paper presents a mixed-integer linear programming model to solve the problem of allocating voltage regulators and fixed or switched capacitors (VRCs) in radial distribution systems. The use of a mixed-integer linear model guarantees convergence to optimality using existing optimization software. In the proposed model, the steady-state operation of the radial distribution system is modeled through linear expressions. The results of one test system and one real distribution system are presented in order to show the accuracy as well as the efficiency of the proposed solution technique. An heuristic to obtain the Pareto front for the multiobjective VRCs allocation problem is also presented. © 2012 Elsevier Ltd. All rights reserved.

The optimal lysine and threonine intake for Cobb broiler breeder hens using Reading model

This study aimed to determine the optimal intake of lysine and threonine for broiler breeder hens. Two experiments were conducted to evaluate the responses of birds to digestible lysine (Lys) and threonine (Thr). Eight treatments were assessed in both experiments, with six replicates of eight birds in the Lys experiment and ten birds in the Thr experiment. The dietary levels of Lys and Thr were obtained by a dilution technique. The experimental period was ten weeks for each amino acid studied, which included six weeks of adaptation and four weeks of data collection. The amino acid intake, egg mass and body weight were adjusted using a Reading model. Based on the model coefficients, the cost of the synthetic amino acids sources and the price of fertile eggs determined the intake of each amino acid to maximize. The minimum intake of Lys and Thr reduced egg production by 40 and 30%, respectively, the weight of the eggs decreased by 12 and 9% with the same intake of Lys and Thr, respectively. The models generated by predicting Lys and Thr intake were as follows: Lys=11 x E+31 x W and Thr=9.5 x E+32 x W, where E=egg mass, g/bird per day, and W=body weight, kg/bird. Based on the models, 3 kg birds with an egg mass production of 50 g/day require 643 mg/bird per day of Lys and 569 mg/bird per day of Thr. The optimum economic intake was calculated at 954 and 834 mg/bird per day for Lys and Thr, respectively, reflecting a dietary concentration of 0.636% Lys and 0.556% Thr for a feed intake of 150 g/bird per day. (C) 2015 Elsevier B.V. All rights reserved.

Optimal clearance of Sporothrix schenckii requires an intact Th17 response in a mouse model of systemic infection

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Stocking of captive-bred fish can cause long-term population decline and gene pool replacement: predictions from a population dynamics model incorporating density-dependent mortality

Releasing captive-bred fish into natural environments (stocking) is common in fisheries worldwide. Although stocking is believed to have a positive effect on fish abundance over the short term, little is known about the long-term consequences of recurrent stocking and its influence on natural populations. In fact, there are growing concerns that genetically maladapted captive-bred fish can eventually reduce the abundance of natural population. In this study, we develop a simple model to quantitatively investigate the condition under which recurrent stocking has long-term effects on the natural population. Using a population dynamics model that takes into account a density-dependent recruitment, a gene responsible for the fitness difference between wild and captive-bred fish, and hybridization between them, we show that there is little or no contribution of recurrent stocking to the stock enhancement without a replacement of the wild gene pool by the captive-bred gene pool. The model further predicted that stocking of an intermediate level causes a reduction, rather than enhancement, of population size over the long term. The population decline due to stocking was attributed to the fitness disadvantage of captive-bred fish and strong overcompensation at recruitment stage. These results suggest that it would be difficult to simultaneously attain population size recovery and conservation of the local gene pool when captive-bred fish have fitness disadvantage in the wild, although caution is needed when applying the predictions from the simplified model to a specific species or population.

Model experiment on optimal size of a fish stock with environmental uncertainties

We analyze the effect of environmental uncertainties on optimal fishery management in a bio-economic fishery model. Unlike most of the literature on resource economics, but in line with ecological models, we allow the different biological processes of survival and recruitment to be affected differently by environmental uncertainties. We show that the overall effect of uncertainty on the optimal size of a fish stock is ambiguous, depending on the prudence of the value function. For the case of a risk-neutral fishery manager, the overall effect depends on the relative magnitude of two opposing effects, the 'convex-cost effect' and the 'gambling effect'. We apply the analysis to the Baltic cod and the North Sea herring fisheries, concluding that for risk neutral agents the net effect of environmental uncertainties on the optimal size of these fish stocks is negative, albeit small in absolute value. Under risk aversion, the effect on optimal stock size is positive for sufficiently high coefficients of constant relative risk aversion.

New methods for the estimation of Takagi-Sugeno model based extended Kalman filter and its applications to optimal control for nonlinear systems

This paper describes new approaches to improve the local and global approximation (matching) and modeling capability of Takagi–Sugeno (T-S) fuzzy model. The main aim is obtaining high function approximation accuracy and fast convergence. The main problem encountered is that T-S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the application of the T-S method because this type of membership function has been widely used during the last 2 decades in the stability, controller design of fuzzy systems and is popular in industrial control applications. The approach developed here can be considered as a generalized version of T-S identification method with optimized performance in approximating nonlinear functions. We propose a noniterative method through weighting of parameters approach and an iterative algorithm by applying the extended Kalman filter, based on the same idea of parameters’ weighting. We show that the Kalman filter is an effective tool in the identification of T-S fuzzy model. A fuzzy controller based linear quadratic regulator is proposed in order to show the effectiveness of the estimation method developed here in control applications. An illustrative example of an inverted pendulum is chosen to evaluate the robustness and remarkable performance of the proposed method locally and globally in comparison with the original T-S model. Simulation results indicate the potential, simplicity, and generality of the algorithm. An illustrative example is chosen to evaluate the robustness. In this paper, we prove that these algorithms converge very fast, thereby making them very practical to use.

A new approach to fuzzy estimation of Takagi-Sugeno model and its applications to optimal control for nonlinear systems

An efficient approach is presented to improve the local and global approximation and modelling capability of Takagi-Sugeno (T-S) fuzzy model. The main aim is obtaining high function approximation accuracy. The main problem is that T-S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the use of the T-S method because this type of membership function has been widely used during the last two decades in the stability, controller design and are popular in industrial control applications. The approach developed here can be considered as a generalized version of T-S method with optimized performance in approximating nonlinear functions. A simple approach with few computational effort, based on the well known parameters' weighting method is suggested for tuning T-S parameters to improve the choice of the performance index and minimize it. A global fuzzy controller (FC) based Linear Quadratic Regulator (LQR) is proposed in order to show the effectiveness of the estimation method developed here in control applications. Illustrative examples of an inverted pendulum and Van der Pol system are chosen to evaluate the robustness and remarkable performance of the proposed method and the high accuracy obtained in approximating nonlinear and unstable systems locally and globally in comparison with the original T-S model. Simulation results indicate the potential, simplicity and generality of the algorithm.

Assessing the impact of adaptive accessibility on the optimal transport policy implementation by using an integrated land-use/transport model for Madrid

Accessibility is an essential concept widely used to evaluate the impact of land-use and transport strategies in transport and urban planning. Accessibility is typically evaluated by using a transport model or a land-use model independently or successively without a feedback loop, thus neglecting the interaction effects between the two systems and the induced competition effects among opportunities due to accessibility improvements. More than a mere methodological curiosity, failure to account for land- use/transport interactions and the competition effect may result in large underestimation of the policy effects. With the recent development of land-use and transport interaction (LUTI) models, there is a growing interest in using these models to adequately measure accessibility and evaluate its impact. The current study joins this research stream by embedding an accessibility measure in a LUTI model with two main aims. The first aim is to account for adaptive accessibility, namely the adjustment of the potential accessibility due to the effect of competition among opportunities (e.g., workplaces) as a result of improved accessibility. LUTI models are particularly suitable for assessing adaptive accessibility because the competition factor is a function of the number of jobs, which is related to land-use attractiveness and the number of workers which is related, among other factors, to the transport demand. The second aim is to identify the optimal implementation scenario of policy measures on the basis of the potential and adaptive accessibility and analyse the results in terms of social welfare and accessibility. The metropolitan area of Madrid is used as a case-study and two transport policy instruments, namely a cordon toll and bus frequency increase, have been chosen for the simulation study in order to present the usefulness of the approach to urban planners and policy makers. The MARS model (Metropolitan Activity Relocation Simulator) calibrated for Madrid was employed as the analysis tool. The impact of accessibility is embedded in the model through a social welfare function that includes not only costs and benefits to both road users and transport operators, but also costs and benefits for the government and society in general (external costs). An optimisation procedure is performed by the MARS model for maximizing the value of objective function in order to find the best (optimal) policy imp lementations intensity (i.e., price, frequency). Last, the two policy strategies are evaluated in terms of their accessibility. Results show that the accessibility with competition factor influences the optimal policy implementation level and also generates different results in terms of social welfare. In addition, mapping the difference between the potential and the adaptive accessibility indicators shows that the main changes occur in areas where there is a strong competition among land-use opportunities.

Optimal Control Using Feedback Linearization for a Generalized T-S Model

In this paper, a fuzzy feedback linearization is used to control nonlinear systems described by Takagi-Suengo (T-S) fuzzy systems. In this work, an optimal controller is designed using the linear quadratic regulator (LQR). The well known weighting parameters approach is applied to optimize local and global approximation and modelling capability of T-S fuzzy model to improve the choice of the performance index and minimize it. The approach used here can be considered as a generalized version of T-S method. Simulation results indicate the potential, simplicity and generality of the estimation method and the robustness of the proposed optimal LQR algorithm.