Chemical Reactors. Problem 1: A simple ODE (chaos in the atmosphere) (2011-2012 Course)

Wording of problem 1: A simple ODE (chaos in the atmosphere).

Dynamic Visual Servoing With Chaos Control for Redundant Robots

This paper presents a new dynamic visual control system for redundant robots with chaos compensation. In order to implement the visual servoing system, a new architecture is proposed that improves the system maintainability and traceability. Furthermore, high performance is obtained as a result of parallel execution of the different tasks that compose the architecture. The control component of the architecture implements a new visual servoing technique for resolving the redundancy at the acceleration level in order to guarantee the correct motion of both end-effector and joints. The controller generates the required torques for the tracking of image trajectories. However, in order to guarantee the applicability of this technique, a repetitive path tracked by the robot-end must produce a periodic joint motion. A chaos controller is integrated in the visual servoing system and the correct performance is observed in low and high velocities. Furthermore, a method to adjust the chaos controller is proposed and validated using a real three-link robot.

Data analysis using circular causality in networks

Complex systems in causal relationships are known to be circular rather than linear; this means that a particular result is not produced by a single cause, but rather that both positive and negative feedback processes are involved. However, although interpreting systemic interrelationships requires a language formed by circles, this has only been developed at the diagram level, and not from an axiomatic point of view. The first difficulty encountered when analysing any complex system is that usually the only data available relate to the various variables, so the first objective was to transform these data into cause-and-effect relationships. Once this initial step was taken, our discrete chaos theory could be applied by finding the causal circles that will form part of the system attractor and allow their behavior to be interpreted. As an application of the technique presented, we analyzed the system associated with the transcription factors of inflammatory diseases.

Direct Visual Servoing Framework based on Optimal Control for Redundant Joint Structures

This paper presents a new framework based on optimal control to define new dynamic visual controllers to carry out the guidance of any serial link structure. The proposed general method employs optimal control to obtain the desired behaviour in the joint space based on an indicated cost function which determines how the control effort is distributed over the joints. The proposed approach allows the development of new direct visual controllers for any mechanical joint system with redundancy. Finally, authors show experimental results and verifications on a real robotic system for some derived controllers obtained from the control framework.

A Sociocybernetics Data Analysis Using Causality in Tourism Networks

The aim of this paper is to propose a mathematical model to determine invariant sets, set covering, orbits and, in particular, attractors in the set of tourism variables. Analysis was carried out based on a pre-designed algorithm and applying our interpretation of chaos theory developed in the context of General Systems Theory. This article sets out the causal relationships associated with tourist flows in order to enable the formulation of appropriate strategies. Our results can be applied to numerous cases. For example, in the analysis of tourist flows, these findings can be used to determine whether the behaviour of certain groups affects that of other groups and to analyse tourist behaviour in terms of the most relevant variables. Unlike statistical analyses that merely provide information on current data, our method uses orbit analysis to forecast, if attractors are found, the behaviour of tourist variables in the immediate future.