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.

Integrating Hamiltonian systems defined on the Lie groups SO(4) and SO(1,3)

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 E³, the spheres S³ and the hyperboloids H³ 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 is illustrated.

Analysis of efficiency and rationality in a sugar-alcohol mill using hyperboloid a-load and potency

Brazil is the world's largest producer of sugar cane and which in the state of São Paulo concentrate the greatest amount of sugar cane field of the country. The sugar-alcohol sector has the capacity to produce sufficient thermal and electrical energy to be used in their process of production and commercialize of surplus in electricity distribution network. Therefore it is necessary to evaluate the energy efficiency and rationality within the mill. Accordingly this research proposed analyze the sugar-alcohol mill's sectors globally and individually, located in the west center of the São Paulo state, using the valuation methodology employed by the Agência Nacional de Energia Elétrica (ANEEL) in the industries that do not have systems of cogeneration. In this analysis, the hyperboloids of load and potency were applied based on the indexes of potency factor and load factor that allow estimate the efficiency and rationality. © 2013 IEEE.

Programa computacional para análise do faturamento do consumo de energia elétrica através do k-hiperbolóide de carga e potência em empresas frigoríficas abatedoras de bovinos

Pós-graduação em Agronomia (Energia na Agricultura) - FCA