The potential field method and the nonlinear attractor dynamics approach: what are the differences?

One of the most popular approaches to path planning and control is the potential field method. This method is particularly attractive because it is suitable for on-line feedback control. In this approach the gradient of a potential field is used to generate the robot's trajectory. Thus, the path is generated by the transient solutions of a dynamical system. On the other hand, in the nonlinear attractor dynamic approach the path is generated by a sequence of attractor solutions. This way the transient solutions of the potential field method are replaced by a sequence of attractor solutions (i.e., asymptotically stable states) of a dynamical system. We discuss at a theoretical level some of the main differences of these two approaches.

Generating timed trajectories foran autonomous robot

Tese de Doutoramento Programa Doutoral em Engenharia Electrónica e Computadores

Homogenization of scalar field cosmologies

We summarise recent results about the evolution of linear density perturbations in scalar field cosmologies with an exponential potential. We use covariant and gauge invariant perturbation variables and a dynamical systems' approach. We establish under what conditions do the perturbations decay to the future in agreement with the cosmic no-hair conjecture.

Pseudofermion dynamical theory for the spin dynamical correlation functions of the half-filled 1D Hubbard model

A modified version of the metallic-phase pseudofermion dynamical theory (PDT) of the 1D Hubbard model is introduced for the spin dynamical correlation functions of the half-filled 1D Hubbard model Mott– Hubbard phase. The Mott–Hubbard insulator phase PDT is applied to the study of the model longitudinal and transverse spin dynamical structure factors at finite magnetic field h, focusing in particular on the sin- gularities at excitation energies in the vicinity of the lower thresholds. The relation of our theoretical results to both condensed-matter and ultra-cold atom systems is discussed.

Systems biology approaches for the design of novel Saccharomyces cerevisiae winemaking strains for enhanced flavour compounds synthesis

Tese de Doutoramento em Biologia Ambiental e Molecular