Coordination Control of Heterogeneous Compounded-Order Multi-Agent Systems with Communication Delays

Since the complexity of the practical environment, many distributed networked systems can not be illustrated with the integer-order dynamics and only be described as the fractional-order dynamics. Suppose multi-agent systems will show the individual diversity with difference agents, where the heterogeneous (integer-order and fractional-order) dynamics are used to illustrate the agent systems and compose integer-fractional compounded-order systems. Applying Laplace transform and frequency domain theory of the fractional-order operator, consensus of delayed multi-agent systems with directed weighted topologies is studied. Since integer-order model is the special case of fractional-order model, the results in this paper can be extend to the systems with integer-order models. Finally, numerical examples are used to verify our results.Comment: 15pages, 4figure

Cyber-Physical Modeling and Control of Crowd of Pedestrians: A Review and New Framework

Recent advances in modeling and control of crowds of pedestrians are briefly surveyed in this paper. Possibilities of applying fractional calculus in the modeling of crowd of pedestrians have been shortly reviewed and discussed from different aspects such as descriptions of motion, interactions of long range and effects of memory. Control of the crowd of pedestrians have also been formulated using the framework of Cyber-Physical Systems and been realized using networked Segways with onboard emergency response personnels to regulate the velocity and flux of the crowd. Platform for verification of the theoretical results are also provided in this paper.Comment: 16 pages, 3 figure

Stability of Fractional-Order Systems with Rational Orders

This paper deals with stability of a certain class of fractional order linear and nonlinear systems. The stability is investigated in the time domain and the frequency domain. The general stability conditions and several illustrative examples are presented as well.Comment: 25 pages, 9 figures, 73 reference

Analysis of dispersion and propagation properties in a periodic rod using a space-fractional wave equation

This study explores the use of fractional calculus as a possible tool to model wave propagation in complex, heterogeneous media. We illustrate the methodology by focusing on elastic wave propagation in a one-dimensional periodic rod. The governing equations describing the wave propagation problem in inhomogeneous systems typically consist of partial differential equations with spatially varying coefficients. Even for very simple systems, these models require numerical solutions which are computationally expensive and do not provide the valuable insights associated with closed-form solutions. We will show that fractional calculus can provide a powerful approach to develop comprehensive mathematical models of inhomogeneous systems that can effectively be regarded as homogenized models. Although at first glance the mathematics might appear more complex, these fractional order models can allow the derivation of closed-form analytical solutions that provide excellent estimations of the systems' dynamic responses. Equally important, these solutions are valid in a frequency range that goes largely beyond the well-known homogenization limit of traditional integer order approaches, therefore providing a possible route to high-frequency homogenization. More specifically, this study focuses on the analyses of the dispersion and propagation properties of a periodic medium under single-tone harmonic excitation and illustrates the methodology to obtain a space-fractional wave equation capable of capturing the behavior of the physical system. The fractional wave equation and its analytical solution are compared with numerical results obtained via a traditional finite element method in order to assess their validity and evaluate their performance. It is found that the resulting fractional differential models are, in their most general form, of complex and frequency-dependent order

Non-existence of periodic solutions in fractional-order dynamical systems and a remarkable difference between integer and fractional-order derivatives of periodic functions

Using the Mellin transform approach, it is shown that, in contrast with integer-order derivatives, the fractional-order derivative of a periodic function cannot be a function with the same period. The three most widely used definitions of fractional-order derivatives are taken into account, namely, the Caputo, Riemann-Liouville and Grunwald-Letnikov definitions. As a consequence, the non-existence of exact periodic solutions in a wide class of fractional-order dynamical systems is obtained. As an application, it is emphasized that the limit cycle observed in numerical simulations of a simple fractional-order neural network cannot be an exact periodic solution of the system.Comment: 15 pages, 2 figure, submitted for publication: April 27th 2011; accepted: November 24, 201

Variational Procedure for Higher-Derivative Mechanical Models in a Fractional Integral Framework

We present both the Lagrangian and Hamiltonian procedures for treating higher-order equations of motion for mechanical models by adopting the Riemann-Liouville Fractional integral to describe their action. We point out and discuss its efficacy and difficulties. We also present the physical and geometric interpretations for the approach we pursue and present the details of a higher-order harmonic oscillator.Comment: 12 pages, 5 figures. arXiv admin note: text overlap with arXiv:1102.453

A Novel Hybrid Fast Switching Adaptive No Delay Tanlock Loop Frequency Synthesizer

This paper presents a new fast switching hybrid frequency synthesizer with wide locking range. The hybrid synthesizer is based on the tanlock loop with no delay block (NDTL) and is capable of integer as well as fractional frequency division. The system maintains the in-lock state following the division process using an efficient adaptation mechanism. The fast switching and acquisition as well as the wide locking range and the robust jitter performance of the new hybrid NDTL synthesizer outperforms conventional time-delay tanlock loop (TDTL) synthesizer by orders of magnitude, making it attractive for synthesis even in Doppler environment. The performance of the hybrid synthesizer was evaluated under various conditions and the results demonstrate that it achieves the desired frequency division

A Fractional Micro-Macro Model for Crowds of Pedestrians based on Fractional Mean Field Games

Modeling of crowds of pedestrians has been considered in this paper from different aspects. Based on fractional microscopic model that may be much more close to reality, a fractional macroscopic model has been proposed using conservation law of mass. Then in order to characterize the competitive and cooperative interactions among pedestrians, fractional mean field games are utilized in the modeling problem when the number of pedestrians goes to infinity and fractional dynamic model composed of fractional backward and fractional forward equations are constructed in macro scale. Fractional micro-macro model for crowds of pedestrians are obtained in the end. Simulation results are also included to illustrate the proposed fractional microscopic model and fractional macroscopic model respectively.Comment: 16 pages, 13 figure

Identification of an Open-loop Plasma Vertical Position Using Fractional Order Dynamic Neural Network

In order to identify complicated systems, more prominent and promising methods are needed among which we may refer to fractional order differential equations. The aim of this paper is to propose a fractional order nonlinear model to predict the vertical position of a plasma column system in a Tokamak by using real data from Damavand Tokamak. The system is identified based on a newly introduced fractional order dynamic neural network. The proposed fractional order dynamic neural network (FODNN) is an extension of the integer order dynamic neural network that employs the so called fractional-order operators. FODNN is implemented and comparison of the numerical simulation results with experimental results shows that performance of the proposed method by using fractional order neural network is preferred to the integer neural network.Comment: 20 pages,8 figure

Cyber-Physical Systems as General Distributed Parameter Systems: Three Types of Fractional Order Models and Emerging Research Opportunities

Cyber-physical systems (CPSs) are man-made complex systems coupled with natural processes that, as a whole, should be described by distributed parameter systems (DPSs) in general forms. This paper presents three such general models for generalized DPSs that can be used to characterize complex CPSs. These three different types of fractional operators based DPS models are: fractional Laplacian operator, fractional power of operator or fractional derivative. This research investigation is motivated by many fractional order models describing natural, physical, and anomalous phenomena, such as sub-diffusion process or super-diffusion process. The relationships among these three different operators are explored and explained. Several potential future research opportunities are then articulated followed by some conclusions and remarks.Comment: 12 pages, 0 figures, IEEE/CAA Journal of Automatica Sinica, 201