arXiv subjects

YangQuan Chen

Publications and source records attributed to YangQuan Chen.

At least 55 records · Page 3Linked to original sources

arXiv2016

Fractional Calculus In Image Processing: A Review

Over the last decade, it has been demonstrated that many systems in science and engineering can be modeled more accurately by fractional-order than integer-order derivatives, and many methods are developed to solve the problem of fractional systems. Due to the extra free parameter order, fractional-order based methods provide additional degree of freedom in optimization performance. Not surprisingly, many fractional-order based methods have been used in image processing field. Herein recent studies are reviewed in ten sub-fields, which include image enhancement, image denoising, image edge detection, image segmentation, image registration, image recognition, image fusion, image encryption, image compression and image restoration. In sum, it is well proved that as a fundamental mathematic tool, fractional-order derivative shows great success in image processing.

cs.CV↗

arXiv2016

On the regional gradient observability of time fractional diffusion processes

This paper for the first time addresses the concepts of regional gradient observability for the Riemann-Liouville time fractional order diffusion system in an interested subregion of the whole domain without the knowledge of the initial vector and its gradient. The Riemann-Liouville time fractional order diffusion system which replaces the first order time derivative of normal diffusion system by a Riemann-Liouville time fractional order derivative of order $α\in (0,1]$ is used to well characterize those anomalous sub-diffusion processes. The characterizations of the strategic sensors when the system under consideration is regional gradient observability are explored. We then describe an approach leading to the reconstruction of the initial gradient in the considered subregion with zero residual gradient vector. At last, to illustrate the effectiveness of our results, we present several application examples where the sensors are zone, pointwise or filament ones.

math.OC↗

arXiv2016

Regional controllability analysis of fractional diffusion equations with Riemann-Liouville time fractional derivatives

This paper is concerned with the concepts of regional controllability for the Riemann-Liouville time fractional diffusion systems of order $α\in(0,1)$. The characterizations of strategic actuators to achieve regional controllability are investigated when the control inputs emerge in the differential equations as distributed inputs. In the end, an approach to guarantee the regional controllability of the problems under consideration in the considered subregion with minimum energy control is described and successfully tested through two applications.

math.OC↗

arXiv2016

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.

nlin.AO↗

arXiv2016

Regional boundary controllability of time fractional diffusion processes

In this paper, we are concerned with the regional boundary controllability of the Riemann-Liouville time fractional diffusion systems of order $α\in (0,1]$. The characterizations of strategic actuators are established when the systems studied are regionally boundary controllable. The determination of control to achieve regional boundary controllability with minimum energy is explored. We also show a connection between the regional internal controllability and regional boundary controllability. Several useful results for the optimal control from an implementation point of view are presented in the end.

math.OC↗

arXiv2015

Global Padé approximations of the generalized Mittag-Leffler function and its inverse

This paper proposes a global Padé approximation of the generalized Mittag-Leffler function $E_{α,β}(-x)$ with $x\in[0,+\infty)$. This uniform approximation can account for both the Taylor series for small arguments and asymptotic series for large arguments. Based on the complete monotonicity of the function $E_{α,β}(-x)$, we work out the global Padé approximation [1/2] for the particular cases $\{0<α<1, β>α\}$, $\{0<α=β<1\}$, and $\{α=1, β>1\}$, respectively. Moreover, these approximations are inverted to yield a global Padé approximation of the inverse generalized Mittag-Leffler function $-L_{α,β}(x)$ with $x\in(0,1/Γ(β)]$. We also provide several examples with selected values $α$ and $β$ to compute the relative error from the approximations. Finally, we point out the possible applications using our established approximations in the ordinary and partial time-fractional differential equations in the sense of Riemann-Liouville.

math.CA↗

arXiv2015

A review and evaluation of numerical tools for fractional calculus and fractional order control

In recent years, as fractional calculus becomes more and more broadly used in research across different academic disciplines, there are increasing demands for the numerical tools for the computation of fractional integration/differentiation, and the simulation of fractional order systems. Time to time, being asked about which tool is suitable for a specific application, the authors decide to carry out this survey to present recapitulative information of the available tools in the literature, in hope of benefiting researchers with different academic backgrounds. With this motivation, the present article collects the scattered tools into a dashboard view, briefly introduces their usage and algorithms, evaluates the accuracy, compares the performance, and provides informative comments for selection.

eess.SY↗

arXiv2015

Fractional-order Generalized Principle of Self-Support (FOG PSS) in Control Systems Design

This paper reviews research that studies the principle of self-support (PSS) in some control systems and proposes a fractional-order generalized PSS framework for the first time. The existing PSS approach focuses on practical tracking problem of integer-order systems including robotic dynamics, high precision linear motor system, multi-axis high precision positioning system with unmeasurable variables, imprecise sensor information, uncertain parameters and external disturbances. More generally, by formulating the fractional PSS concept as a new generalized framework, we will focus in the possible fields on the fractional-order control problems such as practical tracking, $λ$-tracking, etc. of robot systems, multiple mobile agents, discrete dynamical systems, time delay systems and other uncertain nonlinear systems. Finally, the practical tracking of a first-order uncertain model of automobile is considered as a simple example to demonstrate the efficiency of the fractional-order generalized principle of self-support (FOGPSS) control strategy.

eess.SY↗

arXiv2015

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.

math.CA↗

arXiv2015

Regional controllability of anomalous diffusion generated by the time fractional diffusion equations

This paper is concerned with the investigation of the regional controllability of the time fractional diffusion equations. First, some preliminaries and definitions of regional controllability of the system under consideration are introduced, which promote the existence contributions on controllability analysis. Then we analyze the regional controllability with minimum energy of the time fractional diffusion equations on two cases: $B\in \mathbf{L}\left(\mathbf{R}^m, L^2(Ω) \right)$ and $B\notin \mathbf{L}\left(\mathbf{R}^m, L^2(Ω) \right)$. In the end, two applications are given to illustrate our obtained results.

math.OC↗

arXiv2015

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.

physics.soc-ph↗

arXiv2014

Multi-UAV-based Optimal Crop-dusting of Anomalously Diffusing Infestation of Crops

This paper presents a UAV-based optimal crop-dusting method to control anomalously diffusing infestation of crops. Two anomalous diffusion models are considered, which are, respectively, time-fractional order diffusion equation and space-fractional order diffusion equation. Our problem formulation is motivated by real-time pest management by using networked unmanned cropdusters where the pest spreading is modeled as a fractional diffusion equation. We attempt to solve the optimal dynamic location of actuators by using Centroidal Voronoi Tessellations. A new simulation platform (FO-DiffMAS-2D) for measurement scheduling and controls in fractional order distributed parameter systems is also introduced in this paper. Simulation results are presented to show the effectiveness of the proposed method as well as the role of fractional order in the overall control performance.

eess.SY↗

arXiv2014

Further clarifications of "Necessary and sufficient stability condition of fractional-order interval linear systems"

This technical report replies to the comments of [2] in detail, and corrects a possible mis-interpretation of [1] in terms of the conventional robust stability concept. After defining the robust stability and quadratic stability concepts, it will be more clearly described that the condition established in [1] can be considered an exact condition for the quadratic stability of fractional-order interval systems.

math.OC↗

arXiv2013

Optimal random search, fractional dynamics and fractional calculus

What is the most efficient search strategy for the random located target sites subject to the physical and biological constraints? Previous results suggested the Lévy flight is the best option to characterize this optimal problem, however, which ignores the understanding and learning abilities of the searcher agents. In the paper we propose the Continuous Time Random Walk (CTRW) optimal search framework and find the optimum for both of search length's and waiting time's distributions. Based on fractional calculus technique, we further derive its master equation to show the mechanism of such complex fractional dynamics. Numerous simulations are provided to illustrate the non-destructive and destructive cases.

math.OC↗

arXiv2013

A Dynamic-Order Fractional Dynamic System

Multi-system interaction is an important and difficult problem in physics. Motivated by the experimental result of an electronic circuit element "Fractor", we introduce the concept of dynamic-order fractional dynamic system, in which the differential-order of a fractional dynamic system is determined by the output signal of another dynamic system. The new concept offers a comprehensive explanation of physical mechanism of multi-system interaction. The properties and potential applications of dynamic-order fractional dynamic systems are further explored with the analysis of anomalous relaxation and diffusion processes.

math-ph↗

arXiv2012

Stability Analysis of Linear Time-Invariant Distributed-Order Systems

Bounded-input bounded-output stability condition of linear time invariant (LTI) distributed-order system over integral interval $(0,1)$ has been established for the first time. Two cases about weighting function of the distributed order are investigated, and sufficient and necessary conditions of stability for these two types of distributed-order systems are derived. Based on the complex integration analysis, time-domain responses of distributed-order systems are also given by analytical method, and numerical examples are presented to illustrate the proposed conditions.

eess.SY↗

arXiv2012

Stability of fractional-order linear time-invariant system with noncommensurate orders

Bounded-input bounded-output stability conditions for fractional-order linear time-invariant (LTI) system with multiple noncommensurate orders have been established in this paper. The orders become noncommensurate orders when they do not have a common divisor. Sufficient and necessary conditions of stability for this kind of fractional-order LTI system with multiple noncommensurate orders. Based on the numerical inverse Laplace transform technique, time-domain responses for a fractional-order system with double noncommensurate orders are presented to illustrate the obtained stability results.

eess.SY↗

arXiv2012

Impulse response of a generalized fractional second order filter

The impulse response of a generalized fractional second order filter of the form ${{({{s}^{2α}}+a{{s}^α}+b)}^{-γ}}$ is derived, where $0<α\le 1$, $0<γ<2$. The asymptotic properties of the impulse responses are obtained for two cases, and the two cases show the similar properties for the changing of $γ$ values. It is shown that only when ${{({{s}^{2α}}+a{{s}^α}+b)}^{-1}}$ has the critical stability, the generalized fractional second order filter ${{({{s}^{2α}}+a{{s}^α}+b)}^{-γ}}$ has different properties as we change the value of $γ$. Finally, numerical examples to illustrate the impulse response are provided to verify the proposed concepts.

eess.SY↗