OPTIMALITY ON HOMOGENEOUS SPACES, AND THE ANGLE SYSTEM ASSOCIATED WITH A BILINEAR CONTROL SYSTEM

Autor(es)

Ayala, V. ^{[1, 2]} ; Rodriguez, J. C. ^[1] ; San Martin, L. A. B. ^[3]

Afiliação do(s) autor(es)

^[1] Univ Catolica Norte, Dept Matemat, Antofagasta - Chile

^[2] Univ Fed Amazonas, Inst Ciencias Exatas, Manaus - Brazil

^[3] Univ Estadual Campinas, Inst Matemat Estatist & Ciencias Comp, BR-13081970 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: SIAM JOURNAL ON CONTROL AND OPTIMIZATION; v. 48, n. 4, p. 2636-2650, 2009.
• Citações Web of Science: 2

Resumo

Let G be a Lie group. In order to study optimal control problems on a homogeneous space G/H, we identify its cotangent bundle T{*}G/H as a subbundle of the cotangent bundle of G. Next, this identification is used to describe the Hamiltonian lifting of vector fields on G/H induced by elements in the Lie algebra g of G. As an application, we consider a bilinear control system Sigma in R(2) whose matrices generate sl(2). Through the Pontryagin maximum principle, we analyze the time-optimal problem for the angle system P Sigma defined by the projection of S onto the projective line Sigma(1). We compute some examples, and in particular we show that the bang-bang principle does not need to be true. (AU)

• Processo FAPESP: 07/06896-5 - Geometria de sistemas de controle, sistemas dinâmicos e estocásticos
• Beneficiário: Luiz Antonio Barrera San Martin
• Modalidade de apoio: Auxílio à Pesquisa - Temático