Formas triangulares para sistemas não-lineares com duas entradas e controle de sistemas sem arrasto em SU(n) com aplicações em mecânica quântica.

Abstract

Minha mais profunda gratidão aos meus orientadores, Prof. Dr. Paulo Sérgio Pereira da Silva e Prof. Dr. Pierre Rouchon, por me aceitarem como aluno, por estarem constantemente presentes, por me guiarem com paciência e segurança, pela generosidade em ensinar e em remover minhas dúvidas, pelas incontáveis vezes em que passamos horas e horas conversando, discutindo e preenchendo todo o quadro com esboços de novas idéias (os rabiscos no quadro pareciam uma obra de arte!), pelo comprometimento em realizar estudos do mais alto nível acadêmico, pela gentileza e amizade, e por sempre me mostrarem o quanto ainda tenho que aprender quando eu, erroneamente, acho que sei alguma coisa. Sinto-me privilegiado por ser aluno de mestres como vocês. Muito obrigado! A CAPES, pelo financiamento integral da presente tese e pela oportunidade em realizar um estágio de doutorado na França sob a orientação do Prof. Dr. Pierre Rouchon.

A flat triangular form for nonlinear systems with two inputs: Necessary and sufficient conditions

“…To the best of the authors' knowledge, the first work in the literature that considered and characterized the triangular form (3) was the thesis [4, Teorema 3.10, p. 51] of one of the authors. The present paper slightly improves the results of [4] and illustrates the constructive aspects of the results in the examples. Lastly, [5] provides necessary and sufficient conditions for a multi-input nonlinear system to be described, after a change of coordinates, by a flat triangular canonical form which differs from (3).…”

Multi-input control-affine systems static feedback equivalent to a triangular form and their flatness

“…Our main results describing control-affine systems locally static feedback equivalent to the triangular form compatible to the chained form and to the m-chained form, are given by the two following theorems corresponding to two-input control-affine systems, i.e., m = 1 (Theorem 1), and to control-affine systems with m + 1 inputs, for m ≥ 2 (Theorem 2). Let us first consider the case m = 1, which has also been solved, using the formalism of differential forms and codistributions, by (Silveira, 2010) and by (Silveira et al, 2013).…”

Periodic Trajectory Tracking for Control-Affine Driftless Systems on Compact Lie Groups

“…The present work addresses the problem of periodic trajectory tracking for control-affine driftless systems, specifically in the case when the ambient manifold is a Lie group G (which we will further assume to be compact and connected) and the system is left-invariant (see below). It is heavily inspired by [7] (see also its first author's PhD thesis [6]), in which the problem is studied in SU(n) aiming applications to Quantum Computing, and can indeed be considered as a (tentative) extension of their methods to abstract Lie groups. We do not, however, rely on any of their results or even notations directly, but rather on their ideas; nor we aim at any applications whatsoever.…”