Fractional dynamics of a system with particles subjected to impacts

This paper studies the dynamics of a system composed of a collection of particles that exhibit collisions between them. Several entropy measures and different impact conditions of the particles are tested. The results reveal a Power Law evolution both of the system energy and the entropy measures, typical in systems having fractional dynamics.

Intrinsic fractal dynamics in the respiratory system by means of pressure-volume loops

This contribution presents novel concepts for analysis of pressure–volume curves, which offer information about the time domain dynamics of the respiratory system. The aim is to verify whether a mapping of the respiratory diseases can be obtained, allowing analysis of (dis)similarities between the dynamical pattern in the breathing in children. The groups investigated here are children, diagnosed as healthy, asthmatic, and cystic fibrosis. The pressure–volume curves have been measured by means of the noninvasive forced oscillation technique during breathing at rest. The geometrical fractal dimension is extracted from the pressure–volume curves and a power-law behavior is observed in the data. The power-law model coefficients are identified from the three sets and the results show that significant differences are present between the groups. This conclusion supports the idea that the respiratory system changes with disease in terms of airway geometry, tissue parameters, leading in turn to variations in the fractal dimension of the respiratory tree and its dynamics.

Laxity dynamics and LLF schedulability analysis on multiprocessor platforms

LLF (Least Laxity First) scheduling, which assigns a higher priority to a task with a smaller laxity, has been known as an optimal preemptive scheduling algorithm on a single processor platform. However, little work has been made to illuminate its characteristics upon multiprocessor platforms. In this paper, we identify the dynamics of laxity from the system’s viewpoint and translate the dynamics into LLF multiprocessor schedulability analysis. More specifically, we first characterize laxity properties under LLF scheduling, focusing on laxity dynamics associated with a deadline miss. These laxity dynamics describe a lower bound, which leads to the deadline miss, on the number of tasks of certain laxity values at certain time instants. This lower bound is significant because it represents invariants for highly dynamic system parameters (laxity values). Since the laxity of a task is dependent of the amount of interference of higher-priority tasks, we can then derive a set of conditions to check whether a given task system can go into the laxity dynamics towards a deadline miss. This way, to the author’s best knowledge, we propose the first LLF multiprocessor schedulability test based on its own laxity properties. We also develop an improved schedulability test that exploits slack values. We mathematically prove that the proposed LLF tests dominate the state-of-the-art EDZL tests. We also present simulation results to evaluate schedulability performance of both the original and improved LLF tests in a quantitative manner.

Analysis of temperature time-series: embedding dynamics into the MDS method

Global warming and the associated climate changes are being the subject of intensive research due to their major impact on social, economic and health aspects of the human life. Surface temperature time-series characterise Earth as a slow dynamics spatiotemporal system, evidencing long memory behaviour, typical of fractional order systems. Such phenomena are difficult to model and analyse, demanding for alternative approaches. This paper studies the complex correlations between global temperature time-series using the Multidimensional scaling (MDS) approach. MDS provides a graphical representation of the pattern of climatic similarities between regions around the globe. The similarities are quantified through two mathematical indices that correlate the monthly average temperatures observed in meteorological stations, over a given period of time. Furthermore, time dynamics is analysed by performing the MDS analysis over slices sampling the time series. MDS generates maps describing the stations’ locus in the perspective that, if they are perceived to be similar to each other, then they are placed on the map forming clusters. We show that MDS provides an intuitive and useful visual representation of the complex relationships that are present among temperature time-series, which are not perceived on traditional geographic maps. Moreover, MDS avoids sensitivity to the irregular distribution density of the meteorological stations.

Dynamics of a backlash chain

This paper studies the dynamical properties of a system with distributed backlash and impact phenomena. This means that it is considered a chain of masses that interact with each other solely by means of backlash and impact phenomena. It is observed the emergence of non-linear phenomena resembling those encountered in the Fermi-Pasta-Ulam problem.

Analysis of the respiratory dynamics during normal breathing by means of pseudo phase plots and pressure-volume loops

This paper reports on the analysis of tidal breathing patterns measured during noninvasive forced oscillation lung function tests in six individual groups. The three adult groups were healthy, with prediagnosed chronic obstructive pulmonary disease, and with prediagnosed kyphoscoliosis, respectively. The three children groups were healthy, with prediagnosed asthma, and with prediagnosed cystic fibrosis, respectively. The analysis is applied to the pressure–volume curves and the pseudophaseplane loop by means of the box-counting method, which gives a measure of the area within each loop. The objective was to verify if there exists a link between the area of the loops, power-law patterns, and alterations in the respiratory structure with disease. We obtained statistically significant variations between the data sets corresponding to the six groups of patients, showing also the existence of power-law patterns. Our findings support the idea that the respiratory system changes with disease in terms of airway geometry and tissue parameters, leading, in turn, to variations in the fractal dimension of the respiratory tree and its dynamics.

Competitive dynamics for behavior coordination in a joint transportation task

We address the problem of coordinating two non-holonomic mobile robots that move in formation while transporting a long payload. A competitive dynamics is introduced that gradually controls the activation and deactivation of individual behaviors. This process introduces (asymmetrical) hysteresis during behavioral switching. As a result behavioral oscillations, due to noisy information, are eliminated. Results in indoor environments show that if parameter values are chosen within reasonable ranges then, in spite of noise in the robots communi- cation and sensors, the overall robotic system works quite well even in cluttered environments. The robots overt behavior is stable and smooth.

Fractional dynamics in liquid manipulation

This paper presents a fractional calculus perspective in the study of signals captured during the movement of a mechanical manipulator carrying a liquid container. In order to study the signals an experimental setup is implemented. The system acquires data from the sensors, in real time, and, in a second phase, processes them through an analysis package. The analysis package runs off-line and handles the recorded data. The results show that the Fourier spectrum of several signals presents a fractional behavior. The experimental study provides useful information that can assist in the design of a control system and the trajectory planning to be used in reducing or eliminating the effect of vibrations.

Visualizing non-linear control system performance by means of multidimensional scaling

This paper addresses the use of multidimensional scaling in the evaluation of controller performance. Several nonlinear systems are analyzed based on the closed loop time response under the action of a reference step input signal. Three alternative performance indices, based on the time response, Fourier analysis, and mutual information, are tested. The numerical experiments demonstrate the feasibility of the proposed methodology and motivate its extension for other performance measures and new classes of nonlinearities.

Fractional-order impulse response of the respiratory system

This paper presents the measurement, frequency-response modeling and identification, and the corresponding impulse time response of the human respiratory impedance and admittance. The investigated adult patient groups were healthy, diagnosed with chronic obstructive pulmonary disease and kyphoscoliosis, respectively. The investigated children patient groups were healthy, diagnosed with asthma and cystic fibrosis, respectively. Fractional order (FO) models are identified on the measured impedance to quantify the respiratory mechanical properties. Two methods are presented for obtaining and simulating the time-domain impulse response from FO models of the respiratory admittance: (i) the classical pole-zero interpolation proposed by Oustaloup in the early 90s, and (ii) the inverse discrete Fourier Transform (DFT). The results of the identified FO models for the respiratory admittance are presented by means of their average values for each group of patients. Consequently, the impulse time response calculated from the frequency response of the averaged FO models is given by means of the two methods mentioned above. Our results indicate that both methods provide similar impulse response data. However, we suggest that the inverse DFT is a more suitable alternative to the high order transfer functions obtained using the classical Oustaloup filter. Additionally, a power law model is fitted on the impulse response data, emphasizing the intrinsic fractal dynamics of the respiratory system.

Fractional analysis of traffic dynamics

This article presents a dynamical analysis of several traffic phenomena, applying a new modelling formalism based on the embedding of statistics and Laplace transform. The new dynamic description integrates the concepts of fractional calculus leading to a more natural treatment of the continuum of the Transfer Function parameters intrinsic in this system. The results using system theory tools point out that it is possible to study traffic systems, taking advantage of the knowledge gathered with automatic control algorithms. Dynamics, Games and Science I Dynamics, Games and Science I Look Inside Other actions Export citation About this Book Reprints and Permissions Add to Papers Share Share this content on Facebook Share this content on Twitter Share this content on LinkedIn

Approximating fractional derivatives in the perspective of system control

The theory of fractional calculus goes back to the beginning of the theory of differential calculus, but its application received attention only recently. In the area of automatic control some work was developed, but the proposed algorithms are still in a research stage. This paper discusses a novel method, with two degrees of freedom, for the design of fractional discrete-time derivatives. The performance of several approximations of fractional derivatives is investigated in the perspective of nonlinear system control.

Simulation and dynamics of freeway traffic

This paper presents the new package entitled Simulator of Intelligent Transportation Systems (SITS) and a computational oriented analysis of traffic dynamics. The SITS adopts a microscopic simulation approach to reproduce real traffic conditions considering different types of vehicles, drivers and roads. A set of experiments with the SITS reveal the dynamic phenomena exhibited by this kind of system. For this purpose a modelling formalism is developed that embeds the statistics and the Laplace transform. The results make possible the adoption of classical system theory tools and point out that it is possible to study traffic systems taking advantage of the knowledge gathered with automatic control algorithms. A complementary perspective for the analysis of the traffic flow is also quantified through the entropy measure.

Complex-order dynamics in hexapod locomotion

This paper studies the dynamics of foot–ground interaction in hexapod locomotion systems. For that objective the robot motion is characterized in terms of several locomotion variables and the ground is modelled through a non-linear spring-dashpot system, with parameters based on the studies of soil mechanics. Moreover, it is adopted an algorithm with foot-force feedback to control the robot locomotion. A set of model-based experiments reveals the influence of the locomotion velocity on the foot–ground transfer function, which presents complex-order dynamics.

Analysis of the Respiratory Dynamics During Normal Breathing by Means of Pseudophase Plots and Pressure–Volume Loops

This paper reports on the analysis of tidal breathing patterns measured during noninvasive forced oscillation lung function tests in six individual groups. The three adult groups were healthy, with prediagnosed chronic obstructive pulmonary disease, and with prediagnosed kyphoscoliosis, respectively. The three children groups were healthy, with prediagnosed asthma, and with prediagnosed cystic fibrosis, respectively. The analysis is applied to the pressure-volume curves and the pseudophase-plane loop by means of the box-counting method, which gives a measure of the area within each loop. The objective was to verify if there exists a link between the area of the loops, power-law patterns, and alterations in the respiratory structure with disease. We obtained statistically significant variations between the data sets corresponding to the six groups of patients, showing also the existence of power-law patterns. Our findings support the idea that the respiratory system changes with disease in terms of airway geometry and tissue parameters, leading, in turn, to variations in the fractal dimension of the respiratory tree and its dynamics.