Necessary conditions of optimality for vector-valued impulsive control problems

A vector-valued impulsive control problem is considered whose dynamics, defined by a differential inclusion, are such that the vector fields associated with the singular term do not satisfy the so-called Frobenius condition. A concept of robust solution based on a new reparametrization procedure is adopted in order to derive necessary conditions of optimality. These conditions are obtained by taking a limit of those for an appropriate sequence of auxiliary standard optimal control problems approximating the original one. An example to illustrate the nature of the new optimality conditions is provided. © 2000 Elsevier Science B.V. All rights reserved.

Strategies, effectiveness and rationale of vector-borne disease control in the pastoralist system of south-western Uganda

In Uganda, control of vector-borne diseases is mainly in form of vector control, and chemotherapy. There have been reports that acaricides are being misused in the pastoralist systems in Uganda. This is because of the belief by scientists that intensive application of acaricide is uneconomical and unsustainable particularly in the indigenous cattle. The objective of this study was to investigate the strategies, rationale and effectiveness of vector-borne disease control by pastoralists. To systematically carry out these investigations, a combination of qualitative and quantitative research methods was used, in both the collection and the analysis of data. Cattle keepers were found to control tick-borne diseases (TBDs) mainly through spraying, in contrast with the control of trypanosomosis for which the main method of control was by chemotherapy. The majority of herders applied acaricides weekly and used an acaricide of lower strength than recommended by the manufacturers. They used very little acaricide wash, and spraying was preferred to dipping. Furthermore, pastoralists either treated sick animals themselves or did nothing at all, rather than using veterinary personnel. Oxytetracycline (OTC) was the drug commonly used in the treatment of TBDs. Nevertheless, although pastoralists may not have been following recommended practices in their control of ticks and tick-borne diseases, they were neither wasteful nor uneconomical and their methods appeared to be effective. Trypanosomosis was not a problem either in Sembabule or Mbarara district. Those who used trypanocides were found to use more drugs than were necessary.

Stability for impulsive control systems

In this paper we extend the notion of the control Lyapounov pair of functions and derive a stability theory for impulsive control systems. The control system is a measure driven differential inclusion that is partly absolutely continuous and partly singular. Some examples illustrating the features of Lyapounov stability are provided.

Closed loop stability of measure-driven impulsive control systems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Necessary conditions for optimal impulsive control problems

A Maximum Principle is derived for a class of optimal control problems arising in midcourse guidance, in which certain controls are represented by measures and, the state trajectories are functions of bounded variation. The optimality conditions improves on previous optimality conditions by allowing nonsmooth data, measurable time dependence, and a possibly time varying constraint set for the conventional controls.

Invariance for Impulsive Control Systems

In this article, we provide invariance conditions for control systems whose dynamics are given by measure driven differential inclusions. The solution concept plays a critical role in the extension of the conventional conditions for the impulsive control context. A couple of examples illustrating the specific features of impulsive control systems are included.

Three-phase tri-state integrated boost inverter with special space vector and dq0 control

This paper presents a three-phase integrated inverter suitable for stand-alone and grid-connected applications. Furthermore, the utilization of the special features of the tri-state coupled with the new space vector modulation allows the converter to present an attractive degree of freedom for the designing of the controllers. Additionally, the control is derived through dq0 transformation, all the system is described and interesting simulation results are available to confirm the proposal. © 2012 IEEE.

A new sufficient condition for optimal impulsive control problems

In this article we introduce the concept of MP-pseudoinvexity for general nonlinear impulsive optimal control problems whose dynamics are specified by measure driven control equations. This is a general paradigm in that, both the absolutely continuous and singular components of the dynamics depend on both the state and the control variables. The key result consists in showing the sufficiency for optimality of the MP-pseudoinvexity. It is proved that, if this property holds, then every process satisfying the maximum principle is an optimal one. This result is obtained in the context of a proper solution concept that will be presented and discussed. © 2012 IEEE.

Optimal impulsive control in a powered Swing-By

This paper studies the problem of applying an impulsive control in a spacecraft that is performing a Swing-By maneuver. The objective is to study the changes in velocity, energy and angular momentum for this maneuver as a function of the three usual parameters of the standard Swing-By plus the three parameters (the magnitude of the impulse, the point of its application and the angle between the impulse and the velocity of the spacecraft) that specify the impulse applied. The dynamics used is the restricted three body problem under the regularization of Lemaitre, made to increase the accuracy of the numerical integration near the primaries. The present research develops an algorithm to calculate the variation of energy and angular momentum in a maneuver where the application of the impulsive control occurs before or after the passage of the spacecraft by the periapsis, but within the sphere of influence of the secondary body and in a non-tangential direction. Using this approach, it is possible to find the best position and direction to apply the impulse to maximize the energy change of the total maneuver. The results showed that the application of the impulse at the periapsis and in the direction of motion of the spacecraft is usually not the optimal solution.

INTEGRAL FUNCTIONALS ON C*-ALGEBRA OF VECTOR-VALUED REGULATED FUNCTIONS

In this paper we deal with the notion of regulated functions with values in a C*-algebra A and present examples using a special bi-dimensional C*-algebra of triangular matrices. We consider the Dushnik integral for these functions and shows that a convenient choice of the integrator function produces an integral homomorphism on the C*-algebra of all regulated functions ([a, b], A). Finally we construct a family of linear integral functionals on this C*-algebra.

On the properness of an impulsive control extension of dynamic optimization problems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Computations of Vector-Valued Siegel Modular Forms

We carry out some computations of vector-valued Siegel modular forms of degree two, weight (k, 2) and level one, and highlight three experimental results: (1) we identify a rational eigenform in a three-dimensional space of cusp forms; (2) we observe that non-cuspidal eigenforms of level one are not always rational; (3) we verify a number of cases of conjectures about congruences between classical modular forms and Siegel modular forms. Our approach is based on Satoh's description of the module of vector-valued Siegel modular forms of weight (k, 2) and an explicit description of the Hecke action on Fourier expansions. (C) 2013 Elsevier Inc. All rights reserved.

Uniform G-Convexity for Vector-Valued Lp Spaces

2000 Mathematics Subject Classification: 46B20.

Aedes aegypti pharate first instar aseasonal quiescence cues anticipatory plasticity with implications for urban vector ecology and control

The eggs of the dengue fever vector Aedes aegypti possess the ability to undergo an extended quiescence period hosting a fully developed first instar larvae within its chorion. As a result of this life history stage, pharate larvae can withstand months of dormancy inside the egg where they depend on stored reserves of maternal origin. This adaptation known as pharate first instar quiescence, allows A. aegypti to cope with fluctuations in water availability. An examination of this fundamental adaptation has shown that there are trade-offs associated with it. ^ Aedes aegypti mosquitoes are frequently associated with urban habitats that may contain metal pollution. My research has demonstrated that the duration of this quiescence and the extent of nutritional depletion associated with it affects the physiology and survival of larvae that hatch in a suboptimal habitat; nutrient reserves decrease during pharate first instar quiescence and alter subsequent larval and adult fitness. The duration of quiescence compromises metal tolerance physiology and is coupled to a decrease in metallothionein mRNA levels. My findings also indicate that even low levels of environmentally relevant larval metal stress alter the parameters that determine vector capacity. ^ My research has also demonstrated that extended pharate first instar quiescence can elicit a plastic response resulting in an adult phenotype distinct from adults reared from short quiescence eggs. Extended pharate first instar quiescence affects the performance and reproductive fitness of the adult female mosquito as well as the nutritional status of its progeny via maternal effects in an adaptive manner, i.e., anticipatory phenotypic plasticity results as a consequence of the duration of pharate first instar quiescence and alternative phenotypes may exist for this mosquito with quiescence serving as a cue possibly signaling the environmental conditions that follow a dry period. M findings may explain, in part, A. aegypti's success as a vector and its geographic distribution and have implications for its vector capacity and control.^