Delay approximation of fractional integrals

This paper explores the calculation of fractional integrals by means of the time delay operator. The study starts by reviewing the memory properties of fractional operators and their relationship with time delay. Based on the time response of the Mittag-Leffler function an approximation of fractional integrals consisting of time delayed samples is proposed. The tuning of the approximation is optimized by means of a genetic algorithm. The results demonstrate the feasibility of the new perspective and the limits of their application.

Load Control Timescales Simulation in a Multi-Agent Smart Grid Platform

Environmental concerns and the shortage in the fossil fuel reserves have been potentiating the growth and globalization of distributed generation. Another resource that has been increasing its importance is the demand response, which is used to change consumers’ consumption profile, helping to reduce peak demand. Aiming to support small players’ participation in demand response events, the Curtailment Service Provider emerged. This player works as an aggregator for demand response events. The control of small and medium players which act in smart grid and micro grid environments is enhanced with a multi-agent system with artificial intelligence techniques – the MASGriP (Multi-Agent Smart Grid Platform). Using strategic behaviours in each player, this system simulates the profile of real players by using software agents. This paper shows the importance of modeling these behaviours for studying this type of scenarios. A case study with three examples shows the differences between each player and the best behaviour in order to achieve the higher profit in each situation.

Integer/fractional decomposition of the impulse response of fractional linear systems

The decomposition of a fractional linear system is discussed in this paper. It is shown that it can be decomposed into an integer order part, corresponding to possible existing poles, and a fractional part. The first and second parts are responsible for the short and long memory behaviors of the system, respectively, known as characteristic of fractional systems.

Efficient Legendre spectral tau algorithm for solving two-sided space-time Caputo fractional advection-dispersion equation

In this paper we present the operational matrices of the left Caputo fractional derivative, right Caputo fractional derivative and Riemann–Liouville fractional integral for shifted Legendre polynomials. We develop an accurate numerical algorithm to solve the two-sided space–time fractional advection–dispersion equation (FADE) based on a spectral shifted Legendre tau (SLT) method in combination with the derived shifted Legendre operational matrices. The fractional derivatives are described in the Caputo sense. We propose a spectral SLT method, both in temporal and spatial discretizations for the two-sided space–time FADE. This technique reduces the two-sided space–time FADE to a system of algebraic equations that simplifies the problem. Numerical results carried out to confirm the spectral accuracy and efficiency of the proposed algorithm. By selecting relatively few Legendre polynomial degrees, we are able to get very accurate approximations, demonstrating the utility of the new approach over other numerical methods.

Bipedal Locomotion: A Fractional CPG for Generating Patterns

Proceedings of the 10th Conference on Dynamical Systems Theory and Applications

Fractional Dynamics Representation in the Pseudo Phase Plane

Proceedings of the 10th Conference on Dynamical Systems Theory and Applications

Modelling and Control of Freeway Traffic

This paper presents the most recent developments of the Simulator of Intelligent Transportation Systems (SITS). The SITS is based on a microscopic simulation approach to reproduce real traffic conditions in an urban or non-urban network. In order to analyse the quality of the microscopic traffic simulator SITS a benchmark test was performed. A dynamical analysis of several traffic phenomena, applying a new modelling formalism based on the embedding of statistics and Laplace transform, is then addressed. The paper presents also a new traffic control concept applied to a freeway traffic system.

Application of Fractional Calculus in Mechatronics

Fractional Calculus (FC) goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades. In the field of dynamical systems theory some work has been carried out but the proposed models and algorithms are still in a preliminary stage of establishment. Having these ideas in mind, the paper discusses a FC perspective in the study of the dynamics and control of mechanical systems.

Cascade Control of a Hexapod Robot

6th International Conference on Climbing and Walking Robots and the Support Technologies for Mobile Machines, Catania, Italy, 17-19 September

Neural control of an autonomous robot

This article aims to apply the concepts associated with artificial neural networks (ANN) in the control of an autonomous robot system that is intended to be used in competitions of robots. The robot was tested in several arbitrary paths in order to verify its effectiveness. The results show that the robot performed the tasks with success. Moreover, in the case of arbitrary paths the ANN control outperforms other methodologies, such as fuzzy logic control (FLC).

Cross-Layer Admission Control to Enhance the Support of Real-Time Applications in WSN

Real-time monitoring applications may be used in a wireless sensor network (WSN) and may generate packet flows with strict quality of service requirements in terms of delay, jitter, or packet loss. When strict delays are imposed from source to destination, the packets must be delivered at the destination within an end-to-end delay (EED) hard limit in order to be considered useful. Since the WSN nodes are scarce both in processing and energy resources, it is desirable that they only transport useful data, as this contributes to enhance the overall network performance and to improve energy efficiency. In this paper, we propose a novel cross-layer admission control (CLAC) mechanism to enhance the network performance and increase energy efficiency of a WSN, by avoiding the transmission of potentially useless packets. The CLAC mechanism uses an estimation technique to preview packets EED, and decides to forward a packet only if it is expected to meet the EED deadline defined by the application, dropping it otherwise. The results obtained show that CLAC enhances the network performance by increasing the useful packet delivery ratio in high network loads and improves the energy efficiency in every network load.

Fractional State Space Analysis of Temperature Time Series

Atmospheric temperatures characterize Earth as a slow dynamics spatiotemporal system, revealing long-memory and complex behavior. Temperature time series of 54 worldwide geographic locations are considered as representative of the Earth weather dynamics. These data are then interpreted as the time evolution of a set of state space variables describing a complex system. The data are analyzed by means of multidimensional scaling (MDS), and the fractional state space portrait (fSSP). A centennial perspective covering the period from 1910 to 2012 allows MDS to identify similarities among different Earth’s locations. The multivariate mutual information is proposed to determine the “optimal” order of the time derivative for the fSSP representation. The fSSP emerges as a valuable alternative for visualizing system dynamics.

Robot Manipulator Systems: Analysis and Control

Manipulator systems are rather complex and highly nonlinear which makes difficult their analysis and control. Classic system theory is veil known, however it is inadequate in the presence of strong nonlinear dynamics. Nonlinear controllers produce good results [1] and work has been done e. g. relating the manipulator nonlinear dynamics with frequency response [2–5]. Nevertheless, given the complexity of the problem, systematic methods which permit to draw conclusions about stability, imperfect modelling effects, compensation requirements, etc. are still lacking. In section 2 we start by analysing the variation of the poles and zeros of the descriptive transfer functions of a robot manipulator in order to motivate the development of more robust (and computationally efficient) control algorithms. Based on this analysis a new multirate controller which is an improvement of the well known “computed torque controller” [6] is announced in section 3. Some research in this area was done by Neuman [7,8] showing tbat better robustness is possible if the basic controller structure is modified. The present study stems from those ideas, and attempts to give a systematic treatment, which results in easy to use standard engineering tools. Finally, in section 4 conclusions are presented.