Filippov's selection theorem and the existence of solutions for optimal control problems in time scales

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On some extension of optimal control theory

Some problems of Calculus of Variations do not have solutions in the class of classic continuous and smooth arcs. This suggests the need of a relaxation or extension of the problem ensuring the existence of a solution in some enlarged class of arcs. This work aims at the development of an extension for a more general optimal control problem with nonlinear control dynamics in which the control function takes values in some closed, but not necessarily bounded, set. To achieve this goal, we exploit the approach of R.V. Gamkrelidze based on the generalized controls, but related to discontinuous arcs. This leads to the notion of generalized impulsive control. The proposed extension links various approaches on the issue of extension found in the literature.

An Empirical Assessment of Optimal Monetary Policy Delegation in the Euro Area

We estimate a New Keynesian DSGE model for the Euro area under alternative descriptions of monetary policy (discretion, commitment or a simple rule) after allowing for Markov switching in policy maker preferences and shock volatilities. This reveals that there have been several changes in Euro area policy making, with a strengthening of the anti-inflation stance in the early years of the ERM, which was then lost around the time of German reunification and only recovered following the turnoil in the ERM in 1992. The ECB does not appear to have been as conservative as aggregate Euro-area policy was under Bundesbank leadership, and its response to the financial crisis has been muted. The estimates also suggest that the most appropriate description of policy is that of discretion, with no evidence of commitment in the Euro-area. As a result although both ‘good luck’ and ‘good policy’ played a role in the moderation of inflation and output volatility in the Euro-area, the welfare gains would have been substantially higher had policy makers been able to commit. We consider a range of delegation schemes as devices to improve upon the discretionary outcome, and conclude that price level targeting would have achieved welfare levels close to those attained under commitment, even after accounting for the existence of the Zero Lower Bound on nominal interest rates.

An Empirical Assessment of Optimal Monetary Policy Delegation in the Euro Area

We estimate a New Keynesian DSGE model for the Euro area under alternative descriptions of monetary policy (discretion, commitment or a simple rule) after allowing for Markov switching in policy maker preferences and shock volatilities. This reveals that there have been several changes in Euro area policy making, with a strengthening of the anti-inflation stance in the early years of the ERM, which was then lost around the time of German reunification and only recovered following the turnoil in the ERM in 1992. The ECB does not appear to have been as conservative as aggregate Euro-area policy was under Bundesbank leadership, and its response to the financial crisis has been muted. The estimates also suggest that the most appropriate description of policy is that of discretion, with no evidence of commitment in the Euro-area. As a result although both ‘good luck’ and ‘good policy’ played a role in the moderation of inflation and output volatility in the Euro-area, the welfare gains would have been substantially higher had policy makers been able to commit. We consider a range of delegation schemes as devices to improve upon the discretionary outcome, and conclude that price level targeting would have achieved welfare levels close to those attained under commitment, even after accounting for the existence of the Zero Lower Bound on nominal interest rates.

The geometry of optimal control solutions on some six dimensional lie groups

This paper examines optimal solutions of control systems with drift defined on the orthonormal frame bundle of particular Riemannian manifolds of constant curvature. The manifolds considered here are the space forms Euclidean space E-3, the spheres S-3 and the hyperboloids H-3 with the corresponding frame bundles equal to the Euclidean group of motions SE(3), the rotation group SO(4) and the Lorentz group SO(1,3). The optimal controls of these systems are solved explicitly in terms of elliptic functions. In this paper, a geometric interpretation of the extremal solutions is given with particular emphasis to a singularity in the explicit solutions. Using a reduced form of the Casimir functions the geometry of these solutions are illustrated.

Analysis of optimal control problems for the incompressible MHD equations and implementation in a finite element multiphysics code

This thesis deals with the study of optimal control problems for the incompressible Magnetohydrodynamics (MHD) equations. Particular attention to these problems arises from several applications in science and engineering, such as fission nuclear reactors with liquid metal coolant and aluminum casting in metallurgy. In such applications it is of great interest to achieve the control on the fluid state variables through the action of the magnetic Lorentz force. In this thesis we investigate a class of boundary optimal control problems, in which the flow is controlled through the boundary conditions of the magnetic field. Due to their complexity, these problems present various challenges in the definition of an adequate solution approach, both from a theoretical and from a computational point of view. In this thesis we propose a new boundary control approach, based on lifting functions of the boundary conditions, which yields both theoretical and numerical advantages. With the introduction of lifting functions, boundary control problems can be formulated as extended distributed problems. We consider a systematic mathematical formulation of these problems in terms of the minimization of a cost functional constrained by the MHD equations. The existence of a solution to the flow equations and to the optimal control problem are shown. The Lagrange multiplier technique is used to derive an optimality system from which candidate solutions for the control problem can be obtained. In order to achieve the numerical solution of this system, a finite element approximation is considered for the discretization together with an appropriate gradient-type algorithm. A finite element object-oriented library has been developed to obtain a parallel and multigrid computational implementation of the optimality system based on a multiphysics approach. Numerical results of two- and three-dimensional computations show that a possible minimum for the control problem can be computed in a robust and accurate manner.

Exchange controls and the transmission of equity market volatility:the case of the UK

The paper investigates the impact that the relaxation of UK exchange controls in October 1979, had on the transmission of equity market volatility from the UK to other major equity markets. It is suggested that the existence of exchange controls in the UK was an important source of market segmentation which disturbed the transmission of shocks from one country to another, even when shocks contained global information. It is found that when a spillover GARCH(1,1) model is estimated for the five years before and after the removal of exchange controls, volatility shocks spill over from the UK to other markets much more strongly after the removal of exchange controls. This appears to suggest that volatility as well as returns have become more closely related since the UK removed exchange controls.

Metabolic Memory Of ß-cells Controls Insulin Secretion And Is Mediated By Camkii.

Ca(2+)/calmodulin-dependent protein kinase II (CaMKII) functions both in regulation of insulin secretion and neurotransmitter release through common downstream mediators. Therefore, we hypothesized that pancreatic ß-cells acquire and store the information contained in calcium pulses as a form of metabolic memory, just as neurons store cognitive information. To test this hypothesis, we developed a novel paradigm of pulsed exposure of ß-cells to intervals of high glucose, followed by a 24-h consolidation period to eliminate any acute metabolic effects. Strikingly, ß-cells exposed to this high-glucose pulse paradigm exhibited significantly stronger insulin secretion. This metabolic memory was entirely dependent on CaMKII. Metabolic memory was reflected on the protein level by increased expression of proteins involved in glucose sensing and Ca(2+)-dependent vesicle secretion, and by elevated levels of the key ß-cell transcription factor MAFA. In summary, like neurons, human and mouse ß-cells are able to acquire and retrieve information.

Cost effectiveness of OptiMal (R) rapid diagnostic test for malaria in remote areas of the Amazon Region, Brazil

Background: In areas with limited structure in place for microscopy diagnosis, rapid diagnostic tests (RDT) have been demonstrated to be effective. Method: The cost-effectiveness of the Optimal (R) and thick smear microscopy was estimated and compared. Data were collected on remote areas of 12 municipalities in the Brazilian Amazon. Data sources included the National Malaria Control Programme of the Ministry of Health, the National Healthcare System reimbursement table, hospitalization records, primary data collected from the municipalities, and scientific literature. The perspective was that of the Brazilian public health system, the analytical horizon was from the start of fever until the diagnostic results provided to patient and the temporal reference was that of year 2006. The results were expressed in costs per adequately diagnosed cases in 2006 U. S. dollars. Sensitivity analysis was performed considering key model parameters. Results: In the case base scenario, considering 92% and 95% sensitivity for thick smear microscopy to Plasmodium falciparum and Plasmodium vivax, respectively, and 100% specificity for both species, thick smear microscopy is more costly and more effective, with an incremental cost estimated at US$ 549.9 per adequately diagnosed case. In sensitivity analysis, when sensitivity and specificity of microscopy for P. vivax were 0.90 and 0.98, respectively, and when its sensitivity for P. falciparum was 0.83, the RDT was more cost-effective than microscopy. Conclusion: Microscopy is more cost-effective than OptiMal (R) in these remote areas if high accuracy of microscopy is maintained in the field. Decision regarding use of rapid tests for diagnosis of malaria in these areas depends on current microscopy accuracy in the field.

An approach of optimal sensitivity applied in the tertiary loop of the automatic generation control

This paper proposes an approach of optimal sensitivity applied in the tertiary loop of the automatic generation control. The approach is based on the theorem of non-linear perturbation. From an optimal operation point obtained by an optimal power flow a new optimal operation point is directly determined after a perturbation, i.e., without the necessity of an iterative process. This new optimal operation point satisfies the constraints of the problem for small perturbation in the loads. The participation factors and the voltage set point of the automatic voltage regulators (AVR) of the generators are determined by the technique of optimal sensitivity, considering the effects of the active power losses minimization and the network constraints. The participation factors and voltage set point of the generators are supplied directly to a computational program of dynamic simulation of the automatic generation control, named by power sensitivity mode. Test results are presented to show the good performance of this approach. (C) 2008 Elsevier B.V. All rights reserved.

Existence of Multiple Solutions for Second Order Boundary Value Problems

We give conditions on f involving pairs of lower and upper solutions which lead to the existence of at least three solutions of the two point boundary value problem y" + f(x, y, y') = 0, x epsilon [0, 1], y(0) = 0 = y(1). In the special case f(x, y, y') = f(y) greater than or equal to 0 we give growth conditions on f and apply our general result to show the existence of three positive solutions. We give an example showing this latter result is sharp. Our results extend those of Avery and of Lakshmikantham et al.

EXISTENCE OF S-ASYMPTOTICALLY omega-PERIODIC SOLUTIONS FOR ABSTRACT NEUTRAL EQUATIONS

A bounded continuous function it u : [0, infinity) -> X is said to be S-asymptotically omega-periodic if lim(t ->infinity)[u(t + omega) - u(t)] = 0. This paper is devoted to study the existence and qualitative properties of S-asymptotically omega-periodic mild solutions for some classes of abstract neutral functional differential equations with infinite delay, Furthermore, applications to partial differential equations are given.

The existence of solutions for impulsive neutral functional differential equations

This work deals with the existence of mild solutions for a class of impulsive functional differential equations of the neutral type associated with the family of linear closed (not necessarily bounded) operators {A(t) : t is an element of 1}. (C) 2009 Elsevier Ltd. All rights reserved.

Existence of asymptotically almost automorphic solutions to some abstract partial neutral integro-differential equations

The paper establishes the existence and uniqueness of asymptotically almost automorphic mild solution to an abstract partial neutral integro-differential equation with unbounded delay. An example is given to illustrate our results. (C) 2008 Elsevier Ltd. All rights reserved.

Existence of solutions for second order partial neutral functional differential equations

We establish existence of mild solutions for a class of abstract second-order partial neutral functional differential equations with unbounded delay in a Banach space.