Sistemas dinâmicos caóticos, teoria de controle e aplicações

Abstract

This work deals with three themes: the qualitative theory of ordinary differential equations and the dynamical systems they define, the theory of control with feedback and without feedback, an important application of control techniques in microscopy. Important results from the field of dynamical systems (such as the Hartman-Grobman Theorem for flows, the Poincaré-Bendixson Theorem and the Hopf Bifurcation Theorem) are stated and, later, support the feedback control of some nonlinear systems of ordinary differential equations; non-feedback control techniques are then also presented in contrast to these others. Finally, in order to understand how control strategies are implemented in practice, the functioning of the controlling mechanisms of the atomic force microscope is studied.