State constraints in optimal impulsive controls

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A maximum principle for infinite time asymptotically stable impulsive dynamic control systems

We consider an infinite horizon optimal impulsive control problems for which a given cost function is minimized by choosing control strategies driving the state to a point in a given closed set C ∞. We present necessary conditions of optimality in the form of a maximum principle for which the boundary condition of the adjoint variable is such that non-degeneracy due to the fact that the time horizon is infinite is ensured. These conditions are given for conventional systems in a first instance and then for impulsive control problems. They are proved by considering a family of approximating auxiliary interval conventional (without impulses) optimal control problems defined on an increasing sequence of finite time intervals. As far as we know, results of this kind have not been derived previously. © 2010 IFAC.

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.

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

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A maximum principle for constrained infinite horizon dynamic control systems

This article presents and discusses a maximum principle for infinite horizon constrained optimal control problems with a cost functional depending on the state at the final time. The main feature of these optimality conditions is that, under reasonably weak assumptions, the multiplier is shown to satisfy a novel transversality condition at infinite time. It is also shown that these conditions can also be obtained for impulsive control problems whose dynamics are given by measure driven differential equations. © 2011 IFAC.

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.

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.

Plasmid-based controls to detect rpoB mutations in Mycobacterium tuberculosis by quantitative polymerase chain reaction-high-resolution melting

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

Phytochrome controls achene germination in Bidens pilosa L. (Asteraceae) by very low fluence response

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

Effect of an impulsive force on vortices in a rotating Bose-Einstein condensate

The effects of a sudden increase and decrease of the interatomic interaction and harmonic-oscillator trapping potential on vortices in a quasi two-dimensional rotating Bose-Einstein condensate are investigated using the mean-field Gross-Pitaevskii equation. We also study the decay of vortices when the rotation of the condensate is suddenly stopped. Upon a free expansion of a rotating BEC with vortices the radius of the vortex core increases more rapidly than the radius of the condensate. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Stability results for impulsive functional differential equations with infinite delay

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

cAMP signaling pathway controls glycogen metabolism in Neurospora crassa by regulating the glycogen synthase gene expression and phosphorylation

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Ambient pH Controls Glycogen Levels by Regulating Glycogen Synthase Gene Expression in Neurospora crassa. New Insights into the pH Signaling Pathway

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

PALEOCLIMATIC CONTROLS ON STABLE OXYGEN AND CARBON ISOTOPES IN CALICHE OF THE ABO FORMATION (PERMIAN), SOUTH-CENTRAL NEW-MEXICO, USA

The stable oxygen and carbon isotopic composition of caliche in fluvial and supratidal rocks of the Abo Formation (Permian), south-central New Mexico, is controlled by palecoclimate and depositional environment. Fluvial caliche consists of low-Mg calcite nodules and vertically oriented tubules that display stage II texture. Micrite matrix support, brecciation, ooids/pisoliths, aveolar-septal texture, and peloids are common in the fluvial caliche and, along with red color and slickensides in the host shale, indicate pedogenesis in a well-oxidized vadose zone. In contrast, periodic waterlogging of the supratidal paleosols, probably due to high water table, is indicated by drab colors, carbonaceous flecks, horizontal rhizoliths, and the paucity of vadose textures in the stage II caliche nodules.Stable oxygen isotopes are similar in the fluvial and supratidal caliches and range from 21.6 to 30.5 parts per thousand (SMOW). The data exhibit a crude bimodality and delta-O-18 enrichment with a decrease in age (higher in the section). Consideration of these data in the context of delta-temperature relations suggests that 1) surface waters responsible for caliche formation increased in delta-O-18 (from roughly -8 to + 1 parts per thousand) over the 18 m.y. time interval that separated the lowest stratigraphic nodule horizon from the highest, 2) the increasing delta-O-18 values also reflect a warming trend (approximately 15-degrees to nearly 30-degrees-C) in the mean monthly temperature over this same time period, with perhaps an associated increase in Permian ocean temperatures, and 3) the significant variation in delta-O-18 from oldest to youngest caliche was probably enhanced by the amount effect, such that as the temperature increased, the amount of precipitation decreased, resulting in high delta-O-18 values.Caliches in the Abo are enriched in heavy carbon (-7.2 to -1.5 part per thousand PDB) compared to that of soil carbonate derived exclusively from C3 plants (-12 part per thousand PDB), and the supratidal caliches contain somewhat heavier carbon compared to the fluvial caliche. The delta-C-13 values for both environments increase with a decrease in caliche age. These results indicate that as the temperature increased and rainfall decreased with time, the level of C3 plant productivity apparently declined, allowing a greater influx of atmospheric CO2 into the soil. This can only occur when soil respiration rates are quite low or at very shallow depths (less than 10 cm), or both. Atmospheric CO2 seems to have invaded the supratidal soils to a somewhat greater extent than the fluvial soils.

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.